Analysis of stability problems via matrix Lyapunov functions
Directory of Open Access Journals (Sweden)
Anatoly A. Martynyuk
1990-01-01
Full Text Available The stability of nonlinear systems is analyzed by the direct Lyapunov's method in terms of Lyapunov matrix functions. The given paper surveys the main theorems on stability, asymptotic stability and nonstability. They are applied to systems of nonlinear equations, singularly-perturbed systems and hybrid systems. The results are demonstrated by an example of a two-component system.
Control design and comprehensive stability analysis of acrobots based on Lyapunov functions
Institute of Scientific and Technical Information of China (English)
LAI Xu-zhi; WU Yun-xin; SHE Jin-hua; WU Min
2005-01-01
A design method for controllers and a comprehensive stability analysis for an acrobat based on Lyapunov functions are presented. Three control laws based on three Lyapunov functions are designed to increase the energy so as to move the acrobot into the unstable inverted equilibrium position, and solve the problem of posture and energy. The concept of a non-smooth Lyapunov function is employed to analyze the stability of the whole system. The validity of this strategy is demonstrated by simulations.
Directory of Open Access Journals (Sweden)
Héctor Armando Durán Peralta
2010-04-01
Full Text Available The stability of reactors having encompassing concentration and temperature parameters, such as continuous flow stirred tank reactors (CSTR, has been widely explored in the literature; however, there are few papers about the stability of tubular reactor having distributed spatial concentration and temperature parameters such as the plow flow tubular reactor (PFTR. This paper analyses the stability of isothermal and non-isothermal PFTR reactors using the Lyapunov functional method. The first order kinetic reaction was selected because one of this paper’s oblectives was to apply Lyapunov functionals to stability analysis of distributed parameter reactors (technique used in electrical engineering systems’ stability analysis. The stability analysis revealed asymptotically stable tempe- rature and concentration profiles for isothermal PFTR, non-isothermal PFTR with kinetic constant independent of temperature and adiabatic non-isothermal PFTR. Analysis revealed an asymptotically stability region for the heat exchange reactor and an uncertain region where it may have oscillations.
Can stability analysis be really simplified? (revisiting Lyapunov, Barbalat, LaSalle and all that)
Barkana, Itzhak
2017-01-01
Even though Lyapunov approach is the most commonly used method for stability analysis, its use has been hindered by the realization that in most applications the so-called Lyapunov derivative is at most negative semidefinite and not negative definite as desired. Many different approaches have been used in an attempt to overcome these difficulties. Until recently, the most widely accepted stability analysis has been based on Barbalat's Lemma which seems to require uniform continuity of practically all signals involved. Recently, stability analysis methods for nonautonomous nonlinear systems have been revisited. Even though new developments based on unknown works of LaSalle attempted to mitigate these continuity conditions, counterexamples are suggested to contradict these results. New analysis shows that these counterexamples, which are making use of well-known mathematical expressions, are actually using them beyond their domain of validity. Therefore, the restrictive condition of uniform continuity required by Barbalat's Lemma and even the milder conditions required by LaSalle's extension of the Invariance Principle to nonautonomous systems can be further mitigated. A new Invariance Principle only required that bounded trajectories cannot pass an infinite distance in finite time. Finally, a new Theorem of Stability, which is formulated as a direct extension and a generalization of Lyapunov's Theorem, not only simplifies the stability analysis of nonlinear systems, but also leads to conclusive results about the system under analysis.
Zhang, Baoyong; Lam, James; Xu, Shengyuan
2015-07-01
This paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays. The distributed delays are assumed to be constant and prescribed. Since a positive-definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite, it is important for constructing relaxed Lyapunov-Krasovskii functionals, which generally lead to less conservative stability criteria. Based on this fact and using two kinds of integral inequalities, a new delay-dependent condition is obtained, which ensures that the distributed delay neural network under consideration is globally asymptotically stable. This stability criterion is then improved by applying the delay partitioning technique. Two numerical examples are provided to demonstrate the advantage of the presented stability criteria.
Sun, Yuming; Wu, Christine Qiong
2012-12-01
Balancing control is important for biped standing. In spite of large efforts, it is very difficult to design balancing control strategies satisfying three requirements simultaneously: maintaining postural stability, improving energy efficiency and satisfying the constraints between the biped feet and the ground. In this article, a proportional-derivative (PD) controller is proposed for a standing biped, which is simplified as a two-link inverted pendulum with one additional rigid foot-link. The genetic algorithm (GA) is used to search for the control gain meeting all three requirements. The stability analysis of such a deterministic biped control system is carried out using the concept of Lyapunov exponents (LEs), based on which, the system stability, where the disturbance comes from the initial states, and the structural stability, where the disturbance comes from the PD gains, are examined quantitively in terms of stability region. This article contributes to the biped balancing control, more significantly, the method shown in the studied case of biped provides a general framework of systematic stability analysis for certain deterministic nonlinear dynamical systems.
Zhang, Hongbin; Feng, Gang
2008-10-01
This paper is concerned with stability analysis and H(infinity) decentralized control of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions. The fuzzy large-scale systems consist of J interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, and the stability analysis is based on Lyapunov functions that are piecewise quadratic. It is shown that the stability of the discrete-time fuzzy large-scale systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The H(infinity) controllers are also designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions. It is demonstrated via numerical examples that the stability and controller synthesis results based on the piecewise quadratic Lyapunov functions are less conservative than those based on the common quadratic Lyapunov functions.
Stability analysis for impulsive fractional hybrid systems via variational Lyapunov method
Yang, Ying; He, Yong; Wang, Yong; Wu, Min
2017-04-01
This paper investigates the stability properties for a class of impulsive Caputo fractional-order hybrid systems with impulse effects at fixed moments. By utilizing the variational Lyapunov method, a fractional variational comparison principle is established. Some stability and instability criteria in terms of two measures are obtained. These results generalize the known ones, extending the corresponding theory of impulsive fractional differential systems. An example is given to demonstrate their effectiveness.
Design and Lyapunov Stability Analysis of a Fuzzy Logic Controller for Autonomous Road Following
Directory of Open Access Journals (Sweden)
Yi Fu
2010-01-01
Full Text Available Autonomous road following is one of the major goals in intelligent vehicle applications. The development of an autonomous road following embedded system for intelligent vehicles is the focus of this paper. A fuzzy logic controller (FLC is designed for vision-based autonomous road following. The stability analysis of this control system is addressed. Lyapunov's direct method is utilized to formulate a class of control laws that guarantee the convergence of the steering error. Certain requirements for the control laws are presented for designers to choose a suitable rule base for the fuzzy controller in order to make the system stable. Stability of the proposed fuzzy controller is guaranteed theoretically and also demonstrated by simulation studies and experiments. Simulations using the model of the four degree of freedom nonholonomic robotic vehicle are conducted to investigate the performance of the fuzzy controller. The proposed fuzzy controller can achieve the desired steering angle and make the robotic vehicle follow the road successfully. Experiments show that the developed intelligent vehicle is able to follow a mocked road autonomously.
Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems
DEFF Research Database (Denmark)
Yahalom, A.; Levitan, J.; Lewkowicz, M.
2011-01-01
to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion...
A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto
2016-05-01
This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
A Lyapunov-Razumikhin approach for stability analysis of logistics networks with time-delays
Dashkovskiy, Sergey; Karimi, Hamid Reza; Kosmykov, Michael
2012-05-01
Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditions that guarantee stability of the network under consideration. Lyapunov-Razumikhin functions and the local small gain condition are utilised to obtain such conditions. Our stability conditions for the logistics network are based on the information about the interconnection properties between logistic locations and their production rates. Finally, numerical results are provided to demonstrate the proposed approach.
Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids
Kabalan, Mahmoud
Microgrid stability studies have been largely based on small-signal linearization techniques. However, the validity and magnitude of the linearization domain is limited to small perturbations. Thus, there is a need to examine microgrids with large-signal nonlinear techniques to fully understand and examine their stability. Large-signal stability analysis can be accomplished by Lyapunov-based mathematical methods. These Lyapunov methods estimate the domain of asymptotic stability of the studied system. A survey of Lyapunov-based large-signal stability studies showed that few large-signal studies have been completed on either individual systems (dc/ac inverters, dc/dc rectifiers, etc.) or microgrids. The research presented in this thesis addresses the large-signal stability of droop-controlled dc/ac inverters and inverter-based microgrids. Dc/ac power electronic inverters allow microgrids to be technically feasible. Thus, as a prelude to examining the stability of microgrids, the research presented in Chapter 3 analyzes the stability of inverters. First, the 13 th order large-signal nonlinear model of a droop-controlled dc/ac inverter connected to an infinite bus is presented. The singular perturbation method is used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd and 1st order models. Each model ignores certain control or structural components of the full order model. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is studied in three different areas: time domain simulations, Lyapunov's indirect method and domain of attraction estimation. The work aims to present the best model to use in each of the three domains of study. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those three areas of
On stability of discontinuous systems via vector Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper deals with the stability of systems with discontinuous righthand side (with solutions in Filippov's sense) via locally Lipschitz continuous and regular vector Lyapunov functions. A new type of "set-valued derivative" of vector Lyapunov functions is introduced, some generalized comparison principles on dis(c)ontinuous systems are shown. Furthermore, Lyapunov stability theory is developed for a class of discontinuous systems based on locally Lipschitz continuous and regular vector Lyapunov functions.
Stability analysis and quasinormal modes of Reissner–Nordstrøm space-time via Lyapunov exponent
Indian Academy of Sciences (India)
PRADHAN PARTHAPRATIM
2016-07-01
We explicitly derive the proper-time (τ ) principal Lyapunov exponent (λp) and coordinate-time (t ) principal Lyapunov exponent $(\\lambda_c)$ for Reissner–Nordstrøm (RN) black hole (BH). We also compute their ratio. For RN space-time, it is shown that the ratio is $(\\lambda_{p}/\\lambda_{c}) = r_{0}/\\sqrt{r^{2}0 − 3Mr_{0} + 2Q^{2}}$ for time-like circulargeodesics and for Schwarzschild BH, it is $(\\lambda_{p}/\\lambda_{c}) = \\sqrt{r_{0}}/\\sqrt{r_{0} − 3M}. We further show that their ratio $\\lambda_{p}/\\lambda_{c}$ may vary from orbit to orbit. For instance, for Schwarzschild BH at the innermost stable circular orbit (ISCO), the ratio is $(\\lambda_{p}/\\lambda_{c})_{|rISCO}=6M = \\sqrt{2}$ and at marginally bound circular orbit (MBCO) the ratio is calculated to be $(\\lambda_{p}/\\lambda_{c})|_{rmb}=4M = 2$. Similarly, for extremal RN BH, the ratio at ISCO is $(\\lambda_{p}/\\lambda_{c})|_{rISCO}=4M = 2\\sqrt{2}/\\sqrt{3}$. We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit, the real and imaginary parts of the quasinormal modes of RN BH is given by the frequency and instability time-scale of the unstable null circular geodesics.
Lyapunov functionals and stability of stochastic functional differential equations
Shaikhet, Leonid
2013-01-01
Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...
Stabilization of nonlinear systems based on robust control Lyapunov function
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Stability of time-delay systems via Lyapunov functions
Directory of Open Access Journals (Sweden)
Carlos F. Alastruey
2002-01-01
Full Text Available In this paper, a Lyapunov function candidate is introduced for multivariable systems with inner delays, without assuming a priori stability for the nondelayed subsystem. By using this Lyapunov function, a controller is deduced. Such a controller utilizes an input–output description of the original system, a circumstance that facilitates practical applications of the proposed approach.
Lyapunov functionals and stability of stochastic difference equations
Shaikhet, Leonid
2011-01-01
This book offers a general method of Lyapunov functional construction which lets researchers analyze the degree to which the stability properties of differential equations are preserved in their difference analogues. Includes examples from physical systems.
Stabilization of discrete nonlinear systems based on control Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
Circular orbits, Lyapunov stability and Manev-type forces
Blaga, Cristina
2016-01-01
In this article we study the stability in the sense of Lyapunov of the circular orbits in the generalized Manev two bodies problem. First, we explore the existence of the circular orbits and determine their radius. Then, using the first integrals of motion we build a positive definite function, known as a Lyapunov function. It's existence proves that the circular orbit is stable in the sense of Lyapunov. In the end, we consider several real systems of two bodies and compare the characteristics of the circular orbits in Newtonian and modified Manev gravitational field, arguing about our possibilities to observe the differences between the motion in these two fields.
Short-time Lyapunov exponent analysis
Vastano, J. A.
1990-01-01
A new technique for analyzing complicated fluid flows in numerical simulations has been successfully tested. The analysis uses short time Lyapunov exponent contributions and the associated Lyapunov perturbation fields. A direct simulation of the Taylor-Couette flow just past the onset of chaos demonstrated that this new technique marks important times during the system evolution and identifies the important flow features at those times. This new technique will now be applied to a 'minimal' turbulent channel.
Short-time Lyapunov exponent analysis
Vastano, J. A.
1990-01-01
A new technique for analyzing complicated fluid flows in numerical simulations has been successfully tested. The analysis uses short time Lyapunov exponent contributions and the associated Lyapunov perturbation fields. A direct simulation of the Taylor-Couette flow just past the onset of chaos demonstrated that this new technique marks important times during the system evolution and identifies the important flow features at those times. This new technique will now be applied to a 'minimal' turbulent channel.
Stabilization of the Ball on the Beam System by Means of the Inverse Lyapunov Approach
Directory of Open Access Journals (Sweden)
Carlos Aguilar-Ibañez
2012-01-01
Full Text Available A novel inverse Lyapunov approach in conjunction with the energy shaping technique is applied to derive a stabilizing controller for the ball on the beam system. The proposed strategy consists of shaping a candidate Lyapunov function as if it were an inverse stability problem. To this purpose, we fix a suitable dissipation function of the unknown energy function, with the property that the selected dissipation divides the corresponding time derivative of the candidate Lyapunov function. Afterwards, the stabilizing controller is directly obtained from the already shaped Lyapunov function. The stability analysis of the closed-loop system is carried out by using the invariance theorem of LaSalle. Simulation results to test the effectiveness of the obtained controller are presented.
Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions
Michel, Anthony N; Liu, Derong
2015-01-01
The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover the following four general topics: - Representation and modeling of dynamical systems of the types described above - Presentation of Lyapunov and Lagrange stability theory for dynamical sy...
Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun
2005-01-01
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
Stability, Resonance and Lyapunov Inequalities for Periodic Conservative Systems
Canada, Antonio
2010-01-01
This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or unconstrained) minimization problems. We provide some new results on the existence and uniqueness of solutions of nonlinear resonant and periodic systems. Finally, we present some new conditions which guarantee the stable boundedness of linear periodic conservative systems.
Mazinan, A H
2016-03-01
The research addresses a Lyapunov-based constrained control strategy to deal with the autonomous space system in the presence of large disturbances. The aforementioned autonomous space system under control is first represented through a dynamics model and subsequently the proposed control strategy is fully investigated with a focus on the three-axis detumbling and the corresponding pointing mode control approaches. The three-axis detumbling mode control approach is designed to deal with the unwanted angular rates of the system to be zero, while the saturations of the actuators are taken into consideration. Moreover, the three-axis pointing mode control approach is designed in the similar state to deal with the rotational angles of the system to be desirable. The contribution of the research is mathematically made to propose a control law in connection with a new candidate of Lyapunov function to deal with the rotational angles and the related angular rates of the present autonomous space system with respect to state-of-the-art. A series of experiments are carried out to consider the efficiency of the proposed control strategy, as long as a number of benchmarks are realized in the same condition to verify and guarantee the strategy performance in both modes of control approaches.
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Lyapunov Criteria for Structural Stability of Supply Chain System
Institute of Scientific and Technical Information of China (English)
LU Ying-jin; TANG Xiao-wo; ZHOU Zong-fang
2004-01-01
In this paper, based on Cobb-Douglas production function, the structural stability of the supply chain system are analyzed by employing Lyapunov criteria. That the supply chain system structure,with the variance of the rate of re-production input funding, becomes unstable is proved. Noticeably, the solutions shows that when the optimal combination of input parameter element, the qualitative properties of supply chain system change and the supply chain system becomes unstable.
Lyapunov analysis: from dynamical systems theory to applications
Cencini, Massimo; Ginelli, Francesco
2013-06-01
The study of deterministic laws of evolution has characterized the development of science since Newton's times. Chaos, namely the manifestation of irregular and unpredictable dynamics (not random but look random [1]), entered the debate on determinism at the end of the 19th century with the discovery of sensitivity to initial conditions, meaning that small infinitesimal differences in the initial state might lead to dramatic differences at later times. Poincaré [2, 3] was the first to realize that solutions of the three-body problem are generically highly sensitive to initial conditions. At about the same time, this property was recognized in geodesic flows with negative curvature by Hadamard [4]. One of the first experimental observations of chaos, as understood much later, was when irregular noise was heard by Van der Pol in 1927 [5] while studying a periodically forced nonlinear oscillator. Nevertheless, it was only with the advent of digital computing that chaos started to attract the interest of the wider scientific community. After the pioneering investigation of ergodicity in a chain of nonlinear oscillators by Fermi, Pasta and Ulam in 1955 [6], it was in the early 1960s that the numerical studies of Lorenz [7] and Hénon and Heiles [8] revealed that irregular and unpredictable motions are a generic feature of low-dimensional nonlinear deterministic systems. The existence and onset of chaos was then rigorously analyzed in several systems. While an exhaustive list of such mathematical proofs is beyond the scope of this preface, one should mention the contributions of Kolmogorov [9, 10], Chirikov [11], Smale [12], Ruelle and Takens [13], Li and Yorke [14] and Feigenbaum [15]. The characteristic Lyapunov exponents introduced by Oseledets in 1968 [16] are the fundamental quantities for measuring the sensitivity to initial conditions. Oseledets' work generalized the concept of Lyapunov stability to irregular trajectories building upon earlier studies of Birkhoff
2013-06-01
STABILITY BY COMPUTING A SINGLE QUADRATIC LYAPUNOV FUNCTION Mehrdad Pakmehr∗ PhD Candidate Decision and Control Laboratory (DCL) School of Aerospace...linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple...Scheduling Control of Gas Turbine Engines: Stability by Computing a Single Quadratic Lyapunov Function 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c
Global stabilization of nonlinear systems based on vector control lyapunov functions
Karafyllis, Iasson
2012-01-01
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.
Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility
Korobeinikov, Andrei
2013-01-01
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility.
Melnik, Andrey V; Korobeinikov, Andrei
2013-04-01
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
A Lyapunov approach to strong stability of semigroups
Paunonen, L.T.; Zwart, Heiko J.
2013-01-01
In this paper we present Lyapunov based proofs for the well-known Arendt–Batty–Lyubich–Vu Theorem for strongly continuous and discrete semigroups. We also study the spectral properties of the limit isometric groups used in the proofs.
Broucke, R.
1982-01-01
It is pointed out that the Lyapunov Characteristic Numbers constitute a new tool for determining stability of trajectories of dynamical systems, or, even more generally, of solutions of systems of ordinary differential equations. In contrast with the characteristic exponents, which apply only to periodic solutions, the Lyapunov Characteristic Numbers apply to arbitrary nonperiodic solutions as well. A description is presented of the numerical experiments which have been made in order to investigate the practical value of the Lyapunov Characteristic Number and the Kolmogorov Entropy for the purpose of estimating the stability of trajectories and/or numerical integration methods in celestial mechanics. It is found that the Lyapunov Characteristic Numbers are extremely useful for the classification of the solutions of nonintegrable dynamical systems, especially in order to distinguish between quasi-periodic and chaotic solutions. However, the Lyapunov Characteristics Numbers do not appear to be useful for the purpose of evaluating numerical integration methods.
Broucke, R.
1982-01-01
It is pointed out that the Lyapunov Characteristic Numbers constitute a new tool for determining stability of trajectories of dynamical systems, or, even more generally, of solutions of systems of ordinary differential equations. In contrast with the characteristic exponents, which apply only to periodic solutions, the Lyapunov Characteristic Numbers apply to arbitrary nonperiodic solutions as well. A description is presented of the numerical experiments which have been made in order to investigate the practical value of the Lyapunov Characteristic Number and the Kolmogorov Entropy for the purpose of estimating the stability of trajectories and/or numerical integration methods in celestial mechanics. It is found that the Lyapunov Characteristic Numbers are extremely useful for the classification of the solutions of nonintegrable dynamical systems, especially in order to distinguish between quasi-periodic and chaotic solutions. However, the Lyapunov Characteristics Numbers do not appear to be useful for the purpose of evaluating numerical integration methods.
The Lyapunov stabilization of satellite equations of motion using integrals
Nacozy, P. E.
1973-01-01
A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.
The Lyapunov stabilization of satellite equations of motion using integrals
Nacozy, P. E.
1973-01-01
A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging method.First,a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time delay.Then,stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system,and after that the Lyapunov function of the averaged It? equation is taken as the optimal linear combination of the corresponding independent first integrals in involution.Finally,the stability of the system is determined by using the largest eigenvalue of the linearized system.Two examples are used to illustrate the proposed procedure and the effects of delayed time on the Lyapunov stability are discussed as well.
Colburn, B. K.; Boland, J. S., III
1976-01-01
A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.
Colburn, B. K.; Boland, J. S., III
1976-01-01
A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.
Blackwell, C. C.
1987-01-01
A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.
Blackwell, C. C.
1987-01-01
A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.
Energy Technology Data Exchange (ETDEWEB)
Blanchini, F. [Universita di Udine (Italy); Carabelli, S. [Politecnico di Torino (Italy)
1994-12-31
We apply a technique recently proposed in literature for the robust stabilization of linear systems with time-varying uncertain parameters to a magnetic levitation system. This technique allows the construction of a polyhedral Lyapunov function and a linear variable-structure stabilizing controller.
A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems
Directory of Open Access Journals (Sweden)
Stojanović Sreten B.
2007-01-01
Full Text Available This paper presents a Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems. Based on the methods, delay-independent stability condition is derived. A numerical example has been working out to show the applicability of results derived.
Stabilization of Parametric Roll Resonance with Active U-Tanks via Lyapunov Control Design
DEFF Research Database (Denmark)
Holden, Christian; Galeazzi, Roberto; Fossen, Thor Inge;
2009-01-01
design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via...
Directory of Open Access Journals (Sweden)
M Seidi
2016-12-01
Full Text Available Lyapunov exponent method is one of the best tools for investigating the range of stability and the transient behavior of the dynamical systems. In beryllium-moderated and heavy water-moderated reactors, photo-neutron plays an important role in dynamic behavior of the reactor. Therefore, stability analysis for changes in the control parameters of the reactor in order to guarantee safety and control nuclear reactor is important. In this work, the range of stability has been investigated using Lyapunov exponent method in response to step, ramp and sinusoidal external reactivities regarding six groups of delayed neutrons plus nine groups of photo-neutrons. The qualitative results are in good agreement with quantitative results of other works
Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilizationof uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robuststability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, show-ing the advanteges of the proposed method.
Stability of stationary barotropic modons by Lyapunov's direct method
Sakuma, H.; Ghil, M.
1990-01-01
A new Liapunov stability condition is formulated for the shallow-water equations, using a gage-variable formalism. This sufficient condition is derived for the class of perturbations that conserve the total mass. It is weaker than existing stability criteria, i.e., it applies to a wider class of flows. Formal stability to infinitesimally small perturbations of arbitrary shape is obtained for two classes of large-scale geophysical flows: pseudo-eastward flow with constant shear, and localized coherent structures of modon type.
Stability of synchronization in coupled time-delay systems using Krasovskii-Lyapunov theory.
Senthilkumar, D V; Kurths, J; Lakshmanan, M
2009-06-01
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general situation (but with a constraint) where all the coefficients of the error equation corresponding to the synchronization manifold are time dependent. These analytical results are also confirmed by the numerical simulation of paradigmatic examples.
Wang, Qiqi; Rigas, Georgios; Esclapez, Lucas; Magri, Luca; Blonigan, Patrick
2016-11-01
Bluff body flows are of fundamental importance to many engineering applications involving massive flow separation and in particular the transport industry. Coherent flow structures emanating in the wake of three-dimensional bluff bodies, such as cars, trucks and lorries, are directly linked to increased aerodynamic drag, noise and structural fatigue. For low Reynolds laminar and transitional regimes, hydrodynamic stability theory has aided the understanding and prediction of the unstable dynamics. In the same framework, sensitivity analysis provides the means for efficient and optimal control, provided the unstable modes can be accurately predicted. However, these methodologies are limited to laminar regimes where only a few unstable modes manifest. Here we extend the stability analysis to low-dimensional chaotic regimes by computing the Lyapunov covariant vectors and their associated Lyapunov exponents. We compare them to eigenvectors and eigenvalues computed in traditional hydrodynamic stability analysis. Computing Lyapunov covariant vectors and Lyapunov exponents also enables the extension of sensitivity analysis to chaotic flows via the shadowing method. We compare the computed shadowing sensitivities to traditional sensitivity analysis. These Lyapunov based methodologies do not rely on mean flow assumptions, and are mathematically rigorous for calculating sensitivities of fully unsteady flow simulations.
H2-Stabilization of the Isothermal Euler Equations:a Lyapunov Function Approach
Institute of Scientific and Technical Information of China (English)
Martin GUGAT; Günter LEUGERING; Simona TAMASOIU; Ke WANG
2012-01-01
The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm.To this end,an explicit Lyapunov function as a weighted and squared H2-norm of a small perturbation of the stationary solution is constructed.The authors show that by a suitable choice of the boundary feedback conditions,the H2-exponential stability of the stationary solution follows.Due to this fact,the system is stabilized over an infinite time interval.Furthermore,exponential estimates for the C1-norm are derived.
Chu, Chia-Chi; Tsai, Hung-Chi; Chang, Wei-Neng
A Lyapunov-based recurrent neural networks unified power flow controller (UPFC) is developed for improving transient stability of power systems. First, a simple UPFC dynamical model, composed of a controllable shunt susceptance on the shunt side and an ideal complex transformer on the series side, is utilized to analyze UPFC dynamical characteristics. Secondly, we study the control configuration of the UPFC with two major blocks: the primary control, and the supplementary control. The primary control is implemented by standard PI techniques when the power system is operated in a normal condition. The supplementary control will be effective only when the power system is subjected by large disturbances. We propose a new Lyapunov-based UPFC controller of the classical single-machine-infinite-bus system for damping enhancement. In order to consider more complicated detailed generator models, we also propose a Lyapunov-based adaptive recurrent neural network controller to deal with such model uncertainties. This controller can be treated as neural network approximations of Lyapunov control actions. In addition, this controller also provides online learning ability to adjust the corresponding weights with the back propagation algorithm built in the hidden layer. The proposed control scheme has been tested on two simple power systems. Simulation results demonstrate that the proposed control strategy is very effective for suppressing power swing even under severe system conditions.
On the asymptotic stability of linear discrete time-delay systems: The Lyapunov approach
Directory of Open Access Journals (Sweden)
Stojanović Sreten B.
2006-01-01
Full Text Available New conditions for the stability of discrete delay systems of the form x (k+1 = Arjx (k + Aix (k-h are presented in the paper. These new delay-independent conditions were derived using an approach based on the second Lyapunov's method. These results are less conservative than some in the existing literature. A numerical example was worked out to show the applicability of the derived results.
Lyapunov stability in an evolutionary game theory model of the labour market
Directory of Open Access Journals (Sweden)
Ricardo Azevedo Araujo
2014-01-01
Full Text Available In this paper the existence and stability of equilibriums in an evolutionary game theory model of the labour market is studied by using the Lyapunov method. The model displays multiple equilibriums and it is shown that the Nash equilibriums of the static game are evolutionary stable equilibrium in the game theory evolutionary set up. A complete characterization of the dynamics of an evolutionary model of the labour market is provided.
Lyapunov stability and its application to systems of ordinary differential equations
Kennedy, E. W.
1979-01-01
An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.
Stability of quantized time-delay nonlinear systems : A Lyapunov-Krasowskii-functional approach
Persis, Claudio De; Mazenc, Frédéric
2009-01-01
Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of time-invariant constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis appl
Stability Analysis of MEMS Gyroscope Dynamic Systems
M. Naser-Moghadasi; S. A. Olamaei; F. Setoudeh
2013-01-01
In this paper, the existence of a common quadratic Lyapunov function for stability analysis of MEMS Gyroscope dynamic systems has been studied then a new method based on stochastic stability of MEMS Gyroscope system has been proposed.
Analysis of the Emergence in Swarm Model Based on Largest Lyapunov Exponent
Directory of Open Access Journals (Sweden)
Yu Wu
2011-01-01
Full Text Available Emergent behaviors of collective intelligence systems, exemplified by swarm model, have attracted broad interests in recent years. However, current research mostly stops at observational interpretations and qualitative descriptions of emergent phenomena and is essentially short of quantitative analysis and evaluation. In this paper, we conduct a quantitative study on the emergence of swarm model by using chaos analysis of complex dynamic systems. This helps to achieve a more exact understanding of emergent phenomena. In particular, we evaluate the emergent behaviors of swarm model quantitatively by using the chaos and stability analysis of swarm model based on largest Lyapunov exponent. It is concluded that swarm model is at the edge of chaos when emergence occurs, and whether chaotic or stable at the beginning, swarm model will converge to stability with the elapse of time along with interactions among agents.
A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter
Directory of Open Access Journals (Sweden)
Yijia Cao
2017-01-01
Full Text Available The three-phase three-wire neutral-point-clamped shunt active power filter (NPC-SAPF, which most adopts classical closed-loop feedback control methods such as proportional-integral (PI, proportional-resonant (PR and repetitive control, can only output 1st–25th harmonic currents with 10–20 kHz switching frequency. The reason for this is that the controller design must make a compromise between system stability and harmonic current compensation ability under the condition of less than 20 kHz switching frequency. To broaden the bandwidth of the compensation current, a Lyapunov stability theory-based control strategy is presented in this paper for NPC-SAPF. The proposed control law is obtained by constructing the switching function on the basis of the mathematical model and the Lyapunov candidate function, which can avoid introducing closed-loop feedback control and keep the system globally asymptotically stable. By means of the proposed method, the NPC-SAPF has compensation ability for the 1st–50th harmonic currents, the total harmonic distortion (THD and each harmonic content of grid currents satisfy the requirements of IEEE Standard 519-2014. In order to verify the superiority of the proposed control strategy, stability conditions of the proposed strategy and the representative PR controllers are compared. The simulation results in MATLAB/Simulink (MathWorks, Natick, MA, USA and the experimental results obtained on a 6.6 kVA NPC-SAPF laboratory prototype validate the proposed control strategy.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Energy Technology Data Exchange (ETDEWEB)
Look, Nicole [Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309 (United States); Arellano, Christopher J.; Grabowski, Alena M.; Kram, Rodger [Department of Integrative Physiology, University of Colorado Boulder, Boulder, Colorado 80309 (United States); McDermott, William J. [The Orthopedic Specialty Hospital, Murray, Utah 84107 (United States); Bradley, Elizabeth [Department of Computer Science, University of Colorado Boulder, Boulder, Colorado 80309, USA and Santa Fe Institute, Santa Fe, New Mexico 87501 (United States)
2013-12-15
In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics.
Analysis of human standing balance by largest lyapunov exponent.
Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang; Taha, Zahari
2015-01-01
The purpose of this research is to analyse the relationship between nonlinear dynamic character and individuals' standing balance by the largest Lyapunov exponent, which is regarded as a metric for assessing standing balance. According to previous study, the largest Lyapunov exponent from centre of pressure time series could not well quantify the human balance ability. In this research, two improvements were made. Firstly, an external stimulus was applied to feet in the form of continuous horizontal sinusoidal motion by a moving platform. Secondly, a multiaccelerometer subsystem was adopted. Twenty healthy volunteers participated in this experiment. A new metric, coordinated largest Lyapunov exponent was proposed, which reflected the relationship of body segments by integrating multidimensional largest Lyapunov exponent values. By using this metric in actual standing performance under sinusoidal stimulus, an obvious relationship between the new metric and the actual balance ability was found in the majority of the subjects. These results show that the sinusoidal stimulus can make human balance characteristics more obvious, which is beneficial to assess balance, and balance is determined by the ability of coordinating all body segments.
He, Jianbin; Yu, Simin; Cai, Jianping
2016-12-01
Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.
Analysis of Lyapunov Method for Control of Quantum States
Wang, Xiaoting; Schirmer, Sonia
2009-01-01
The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined on an extended space where the LaSalle invariance principle can be correctly applied even for non-stationary target states. LaSalle's invariance principle is used to derive a general characterization of the invariant set, which is shown to always contain the...
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Schubert, Sebastian; Lucarini, Valerio
2016-04-01
The classical approach for studying atmospheric variability is based on defining a background state and studying the linear stability of the small fluctuations around such a state. Weakly non-linear theories can be constructed using higher order expansions terms. While these methods have undoubtedly great value for elucidating the relevant physical processes, they are unable to follow the dynamics of a turbulent atmosphere. We provide a first example of extension of the classical stability analysis to a non-linearly evolving quasi-geostrophic flow. The so-called covariant Lyapunov vectors (CLVs) provide a covariant basis describing the directions of exponential expansion and decay of perturbations to the non-linear trajectory of the flow. We use such a formalism to re-examine the basic barotropic and baroclinic processes of the atmosphere with a quasi-geostrophic beta-plane two-layer model in a periodic channel driven by a forced meridional temperature gradient ΔT . We explore three settings of ΔT , representative of relatively weak turbulence, well-developed turbulence, and intermediate conditions. We construct the Lorenz energy cycle for each CLV describing the energy exchanges with the background state. A positive baroclinic conversion rate is a necessary but not sufficient condition of instability. Barotropic instability is present only for few very unstable CLVs for large values of ΔT. Slowly growing and decaying hydrodynamic Lyapunov modes closely mirror the properties of the background flow. Following classical necessary conditions for barotropic/baroclinic instability, we find a clear relationship between the properties of the eddy fluxes of a CLV and its instability. CLVs with positive baroclinic conversion seem to form a set of modes for constructing a reduced model of the atmosphere dynamics.
Smith, Beth A.; Stergiou, Nicholas; Ulrich, Beverly D.
2010-01-01
In previous studies we found that while preadolescents with Down syndrome (DS) produce higher amounts of variability (Smith et al., 2007) and larger Lyapunov exponent (LyE) values (indicating more instability) during walking than peers with typical development (TD) (Buzzi & Ulrich, 2004), they also partition more of this into goal-equivalent variability (UCM//), that can be exploited to increase options for success when perturbed (Black et al., 2007). Here we use nonlinear methods to examine the patterns that characterize gait variability as it emerges, in toddlers with TD and with DS, rather than after years of practice. We calculated Lyapunov exponent (LyE) values to assess stability of leg trajectories. We also tested the use of 3 algorithms for surrogation analysis to investigate mathematical periodicity of toddlers’ strides. Results show that toddlers’ LyE values were not different between groups or with practice and strides of both groups become more periodic with practice. PMID:20237407
Canada, Antonio
2011-01-01
Several different problems make the study of the so called Lyapunov type inequalities of great interest, both in pure and applied mathematics. Although the original historical motivation was the study of the stability properties of the Hill equation (which applies to many problems in physics and engineering), other questions that arise in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients, etc. lead to the study of $L_p$ Lyapunov inequalities ($1\\leq p\\leq \\infty$) for differential equations. In this work we review some recent results on these kinds of questions which can be formulated as optimal control problems. In the case of Ordinary Differential Equations, we consider periodic and antiperiodic boundary conditions at higher eigenvalues and by using a more accurate version of the Sturm separation theory, an explicit optimal result is obtained. Then, we establish Lyapunov inequalities for systems of equations. To this respect, a key point is the characterization of the be...
Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles
Baetens, Jan M.; Gravner, Janko
2016-10-01
We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.
Lyapunov Exponents and Covariant Vectors for Turbulent Flow Simulations
Blonigan, Patrick; Murman, Scott; Fernandez, Pablo; Wang, Qiqi
2016-11-01
As computational power increases, engineers are beginning to use scale-resolving turbulent flow simulations for applications in which jets, wakes, and separation dominate. However, the chaotic dynamics exhibited by scale-resolving simulations poses problems for the conventional sensitivity analysis and stability analysis approaches that are vital for design and control. Lyapunov analysis is used to study the chaotic behavior of dynamical systems, including flow simulations. Lyapunov exponents are the growth or a decay rate of specific flow field perturbations called the Lyapunov covariant vectors. Recently, the authors have used Lyapunov analysis to study the breakdown in conventional sensitivity analysis and the cost of new shadowing-based sensitivity analysis. The current work reviews Lyapunov analysis and presents new results for a DNS of turbulent channel flow, wall-modeled channel flow, and a DNS of a low pressure turbine blade. Additionally, the implications of these Lyapunov analyses for computing sensitivities of these flow simulations will be discussed.
ORIGINAL ARTICLE Stability Analysis of Delayed Cournot Model in ...
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HP
and Lyapunov method of nonlinear stability analysis are employed. It is ascertained ... MATLAB2012a is used to demonstrate the applicability and accuracy of the results. ...... computation, 149(3), 843-860. ... Science and Complexity, Elsevier.
Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors
Energy Technology Data Exchange (ETDEWEB)
Gavilian-Moreno, Carlos [Iberdrola Generacion, S.A., Cofrentes Nuclear Power Plant, Project Engineering Department, Paraje le Plano S/N, Valencia (Spain); Espinosa-Paredes, Gilberto [Area de ingeniera en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Mexico city (Mexico)
2016-04-15
The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.
Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis.
Chung, H-Y; Chung, C-Y; Ou, S-C
2012-10-01
The study will apply Lyapunov principle to construct a dynamic model for tuberculosis (TB). The Lyapunov principle is commonly used to examine and determine the stability of a dynamic system. To simulate the transmissions of vector-borne diseases and discuss the related health policies effects on vector-borne diseases, the authors combine the multi-agent-based system, social network and compartmental model to develop an epidemic simulation model. In the identity level, the authors use the multi-agent-based system and the mirror identity concept to describe identities with social network features such as daily visits, long-distance movement, high degree of clustering, low degree of separation and local clustering. The research will analyse the complex dynamic mathematic model of TB epidemic and determine its stability property by using the popular Matlab/Simulink software and relative software packages. Facing the current TB epidemic situation, the development of TB and its developing trend through constructing a dynamic bio-mathematical system model of TB is investigated. After simulating the development of epidemic situation with the solution of the SMIR epidemic model, the authors will come up with a good scheme to control epidemic situation to analyse the parameter values of a model that influence epidemic situation evolved. The authors will try to find the quarantining parameters that are the most important factors to control epidemic situation. The SMIR epidemic model and the results via numerical analysis may offer effective prevention with reference to controlling epidemic situation of TB.
ROBUST STABILITY ANALYSIS FOR RAILWAY VEHICLE SYSTEMS
Institute of Scientific and Technical Information of China (English)
Wang Yong; Zeng Jing; Cao Dengqing
2003-01-01
The lateral stability for railway vehicle dynamic system with uncertain parameters and nonlinear uncertain force vector is studied by using the Lyapunov stability theory. A robust stability condition for the considered system is derived, and the obtained stability bounds are not necessarily symmetric with respect to the origin in the parameter space. The lateral stability analysis for a railway bogie model is analyzed by using the proposed approach. The symmetric and asymmetric results are both given and the influence of the adjustable parameter ( on the stability bounds is also discussed. With the help of the proposed method, the robust stability analysis can provide a reference for the design of the railway vehicle systems.
Ma, Junhai; Ren, Wenbo; Zhan, Xueli
2017-04-01
Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.
Azizi, Sajad
2017-05-01
The robust stability of a class of feedback linearizable minimum-phase nonlinear system, having parametric uncertainties, is investigated in this study. The system in new coordinates is represented to an equivalent formulation after the attempt of feedback linearization. Due to the parametric uncertainties the approximately linearized system entails a norm bounded input nonlinearity such that the equilibrium point condition in error dynamics can not be satisfied. Accordingly, to guarantee the regional asymptotic stability a control synthesis problem is proposed by means of sufficient Linear Matrix Inequalities (LMIs) together with an amended nonlinear control term, derived from the Lyapunov redesign method, which tackles zero steady-state error condition. The numerical examples of a general aviation aircraft's longitudinal dynamics and inverted pendulum are simulated to show the proficiency of the proposed control technique. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Computational Stability Analysis of Lotka-Volterra Systems
Directory of Open Access Journals (Sweden)
Polcz Péter
2016-12-01
Full Text Available This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4 dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.
Principal component cluster analysis of ECG time series based on Lyapunov exponent spectrum
Institute of Scientific and Technical Information of China (English)
WANG Nai; RUAN Jiong
2004-01-01
In this paper we propose an approach of principal component cluster analysis based on Lyapunov exponent spectrum (LES) to analyze the ECG time series. Analysis results of 22 sample-files of ECG from the MIT-BIH database confirmed the validity of our approach. Another technique named improved teacher selecting student (TSS) algorithm is presented to analyze unknown samples by means of some known ones, which is of better accuracy. This technique combines the advantages of both statistical and nonlinear dynamical methods and is shown to be significant to the analysis of nonlinear ECG time series.
Crauel, Hans; Eckmann, Jean-Pierre
1991-01-01
Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant me...
Schubert, Sebastian
2015-01-01
One of the most relevant weather regimes in the mid latitudes atmosphere is the persistent deviation from the approximately zonally symmetric jet stream to the emergence of so-called blocking patterns. Such configurations are usually connected to exceptional local stability properties of the flow which come along with an improved local forecast skills during the phenomenon. It is instead extremely hard to predict onset and decay of blockings. Covariant Lyapunov Vectors (CLVs) offer a suitable characterization of the linear stability of a chaotic flow, since they represent the full tangent linear dynamics by a covariant basis which explores linear perturbations at all time scales. Therefore, we will test whether CLVs feature a signature of the blockings. We examine the CLVs for a quasi-geostrophic beta-plane two-layer model in a periodic channel baroclinically driven by a meridional temperature gradient $\\Delta T$. An orographic forcing enhances the emergence of localized blocked regimes. We detect the blockin...
Schubert, Sebastian; Lucarini, Valerio
2016-04-01
One of the most relevant weather regimes in the mid latitudes atmosphere is the persistent deviation from the approximately zonally symmetric jet stream to the emergence of so-called blocking patterns. Such configurations are usually connected to exceptional local stability properties of the flow which come along with an improved local forecast skills during the phenomenon. It is instead extremely hard to predict onset and decay of blockings. Covariant Lyapunov Vectors (CLVs) offer a suitable characterization of the linear stability of a chaotic flow, since they represent the full tangent linear dynamics by a covariant basis which explores linear perturbations at all time scales. Therefore, we will test whether CLVs feature a signature of the blockings. We examine the CLVs for a quasi-geostrophic beta-plane two-layer model in a periodic channel baroclinically driven by a meridional temperature gradient ΔT. An orographic forcing enhances the emergence of localized blocked regimes. We detect the blocking events of the channel flow with a Tibaldi-Molteni scheme adapted to the periodic channel. When blocking occurs, the global growth rates of the fastest growing CLVs are significantly higher. Hence against intuition, globally the circulation is more unstable in blocked phases. Such an increase in the finite time Lyapunov exponents with respect to the long term average is attributed to stronger barotropic and baroclinic conversion in the case of high temperature gradients, while for low values of ΔT, the effect is only due to stronger barotropic instability. For the localization of the CLVs, we compare the meridionally averaged variance of the CLVs during blocked and unblocked phases. We find that on average the variance of the CLVs is clustered around the center of blocking. These results show that the blocked flow affects all time scales and processes described by the CLVs.
Directory of Open Access Journals (Sweden)
Coşkun Yakar
2010-01-01
Full Text Available The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.
Institute of Scientific and Technical Information of China (English)
Qiu Fang; Zhang Quan-Xin; Deng Xue-Hui
2012-01-01
This paper investigates the asymptotical stability problem of a neural system with a constant delay.A new delaydependent stability condition is derived by using the novel augmented Lyapunov-Krasovskii function with triple integral terms,and the additional triple integral terms play a key role in the further reduction of conservativeness.Finally,a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
Pakmehr, Mehrdad; Fitzgerald, Nathan; Feron, Eric; Shamma, Jeff; Behbahani, Alireza
2012-01-01
This manuscript aims to develop and describe gain scheduling control concept for a gas turbine engine which drives a variable pitch propeller. An architecture for gain-scheduling control is developed that controls the turboshaft engine for large thrust commands in stable fashion with good performance. Fuel ow and propeller pitch angle are the two control inputs of the system. New stability proof has been developed for gain scheduling control of gas turbine engines using global linearization a...
STABILITY ANALYSIS FOR THE LARGE-SCALE SYSTEMS WITH TIME-DELAY
Institute of Scientific and Technical Information of China (English)
Jingru Qu; Cunchen GAO
2006-01-01
The stability analysis problems were put forward for the large-scale systems with time-delay by using the partial decomposition method. With the stability of the isolated subsystems without time-delay, some sufficient criterions for the asymptotical stability of the whole system were obtained by making a Lyapunov function with the Razumikhin condition and a Lyapunov functional for the retarded type and neutral type, respectively.
Directory of Open Access Journals (Sweden)
Seung Kwan Song
2016-10-01
Full Text Available We present two control strategies for an oscillating water column-wave energy converter (OWC-WEC in the time domain. We consider a fixed OWC-WEC on the open sea with an impulse turbine module. This system mainly consists of a chamber, turbine and electric generator. For the time domain analysis, all of the conversion stages considering mutualities among them should be analyzed based on the Newtonian mechanics. According to the analysis of Newtonian mechanics, the hydrodynamics of wave energy absorption in the chamber and the turbine aerodynamic performance are directly coupled and share the internal air pressure term via the incompressible air assumption. The turbine aerodynamics and the dynamics of the electric generator are connected by torque load through the rotor shaft, which depends on an electric terminal load that acts as a control input. The proposed control strategies are an instant maximum turbine efficiency tracking control and a constant angular velocity of the turbine rotor control methods. Both are derived by Lyapunov stability analysis. Numerical simulations are carried out under irregular waves with various heights and periods in the time domain, and the results with the controllers are analyzed. We then compare these results with simulations carried out in the absence of the control strategy in order to prove the performance of the controllers.
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...
Greenwood, Nigel J C; Gunton, Jenny E
2014-07-01
This study demonstrated the novel application of a "machine-intelligent" mathematical structure, combining differential game theory and Lyapunov-based control theory, to the artificial pancreas to handle dynamic uncertainties. Realistic type 1 diabetes (T1D) models from the literature were combined into a composite system. Using a mixture of "black box" simulations and actual data from diabetic medical histories, realistic sets of diabetic time series were constructed for blood glucose (BG), interstitial fluid glucose, infused insulin, meal estimates, and sometimes plasma insulin assays. The problem of underdetermined parameters was side stepped by applying a variant of a genetic algorithm to partial information, whereby multiple candidate-personalized models were constructed and then rigorously tested using further data. These formed a "dynamic envelope" of trajectories in state space, where each trajectory was generated by a hypothesis on the hidden T1D system dynamics. This dynamic envelope was then culled to a reduced form to cover observed dynamic behavior. A machine-intelligent autonomous algorithm then implemented game theory to construct real-time insulin infusion strategies, based on the flow of these trajectories through state space and their interactions with hypoglycemic or near-hyperglycemic states. This technique was tested on 2 simulated participants over a total of fifty-five 24-hour days, with no hypoglycemic or hyperglycemic events, despite significant uncertainties from using actual diabetic meal histories with 10-minute warnings. In the main case studies, BG was steered within the desired target set for 99.8% of a 16-hour daily assessment period. Tests confirmed algorithm robustness for ±25% carbohydrate error. For over 99% of the overall 55-day simulation period, either formal controller stability was achieved to the desired target or else the trajectory was within the desired target. These results suggest that this is a stable, high
Multiscale analysis of biological data by scale-dependent lyapunov exponent.
Gao, Jianbo; Hu, Jing; Tung, Wen-Wen; Blasch, Erik
2011-01-01
Physiological signals often are highly non-stationary (i.e., mean and variance change with time) and multiscaled (i.e., dependent on the spatial or temporal interval lengths). They may exhibit different behaviors, such as non-linearity, sensitive dependence on small disturbances, long memory, and extreme variations. Such data have been accumulating in all areas of health sciences and rapid analysis can serve quality testing, physician assessment, and patient diagnosis. To support patient care, it is very desirable to characterize the different signal behaviors on a wide range of scales simultaneously. The Scale-Dependent Lyapunov Exponent (SDLE) is capable of such a fundamental task. In particular, SDLE can readily characterize all known types of signal data, including deterministic chaos, noisy chaos, random 1/f(α) processes, stochastic limit cycles, among others. SDLE also has some unique capabilities that are not shared by other methods, such as detecting fractal structures from non-stationary data and detecting intermittent chaos. In this article, we describe SDLE in such a way that it can be readily understood and implemented by non-mathematically oriented researchers, develop a SDLE-based consistent, unifying theory for the multiscale analysis, and demonstrate the power of SDLE on analysis of heart-rate variability (HRV) data to detect congestive heart failure and analysis of electroencephalography (EEG) data to detect seizures.
Beaudette, Shawn M; Howarth, Samuel J; Graham, Ryan B; Brown, Stephen H M
2016-10-01
Several different state-space reconstruction methods have been employed to assess the local dynamic stability (LDS) of a 3D kinematic system. One common method is to use a Euclidean norm (N) transformation of three orthogonal x, y, and z time-series' followed by the calculation of the maximum finite-time Lyapunov exponent (λmax) from the resultant N waveform (using a time-delayed state space reconstruction technique). By essentially acting as a weighted average, N has been suggested to account for simultaneous expansion and contraction along separate degrees of freedom within a 3D system (e.g. the coupling of dynamic movements between orthogonal planes). However, when estimating LDS using N, non-linear transformations inherent within the calculation of N should be accounted for. Results demonstrate that the use of N on 3D time-series data with arbitrary magnitudes of relative bias and zero-crossings cause the introduction of error in estimates of λmax obtained through N. To develop a standard for the analysis of 3D dynamic kinematic waveforms, we suggest that all dimensions of a 3D signal be independently shifted to avoid the incidence of zero-crossings prior to the calculation of N and subsequent estimation of LDS through the use of λmax.
Li, Zhihong; Liu, Lei; Zhu, Quanxin
2016-12-01
This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results. Copyright © 2016 Elsevier Ltd. All rights reserved.
Haddad, Wassim M.; Bernstein, Dennis S.
1991-01-01
Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed.
Haddad, Wassim M.; Bernstein, Dennis S.
1991-01-01
Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed.
DEFF Research Database (Denmark)
Eriksson, Robert
2014-01-01
as possible, and is based on Lyapunov theory considering the nonlinear behavior. The time optimal controller is of a bang-bang type and uses wide-area measurements as feedback signals. Nonlinear simulations are run in the Nordic32 test system implemented in PowerFactory/DIgSILENT with an interface to Matlab...
Stability Analysis of Uncertain Discrete-Time Piecewise Linear Systems with Time Delays
Institute of Scientific and Technical Information of China (English)
Ou Ou; Hong-Bin Zhang; Jue-Bang Yu
2009-01-01
This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.
Directory of Open Access Journals (Sweden)
Mokaedi V. Lekgari
2014-01-01
Full Text Available We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs. We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.
Wang, Zhikang; Lou, Haifang; Sun, Jianzhong
2011-07-01
Attempting to use nonlinear spatiotemporal Lyapunov exponent to characterize fMRI brain functional connectivity of anxiety disease patients, we adopted the methods of nonlinear spatiotemporal Lyapunov exponent and linear correlation coefficients to analyses fMRI datum of 11 anxiety disease patients and 11 healthy volunteers, respectively. The results show that there are significant normalized variance exponent (NVE) differences in Inferior Frontal Gyrus (rIFG) and Medial Frontal Gyrus (MFG) between the two groups (PLyapunov exponent method had higher sensitivity than the correlation coefficient method in the characterization of functional connectivity; Anxiety disease patients have abnormal functional connectivity in rIFG and MFG during our experiment.
Institute of Scientific and Technical Information of China (English)
岑丽辉; 席裕庚
2009-01-01
A Lyapunov function is constructed based on the weighted sum of entropies for the case of two open channels in cascade, which is described by the Saint-Venant equations. A class of boundary feedback controllers is presented to guaran-tee the local closed-loop asymptotic stability in a neighborhood of the equilibrium point by means of the Lyapunov design ap-proach.
Finite-time Lyapunov exponent-based analysis for compressible flows
González, D. R.; Speth, R. L.; Gaitonde, D. V.; Lewis, M. J.
2016-08-01
The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis.
Finite-time Lyapunov exponent-based analysis for compressible flows.
González, D R; Speth, R L; Gaitonde, D V; Lewis, M J
2016-08-01
The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis.
Analisis Kestabilan Model Matematika Penyakit Leukimia dengan Fungsi Lyapunov
2015-01-01
This study aims to analyze the stability of the equilibrium point of the mathematical model of leukemia before and after undergoing chemotherapy. Analysis of the stability of the model is done by analyzing the model by using a Lyapunov function. By using MATLAB program will be described stability of the model before chemotherapy and after chemotherapy. The results showed that the equilibrium point of stem cell compartment model is asymptotically stable for certain parameter values. This is be...
On the Computation of Lyapunov Functions for Interconnected Systems
DEFF Research Database (Denmark)
Sloth, Christoffer
2016-01-01
This paper addresses the computation of additively separable Lyapunov functions for interconnected systems. The presented results can be applied to reduce the complexity of the computations associated with stability analysis of large scale systems. We provide a necessary and sufficient condition...
Directory of Open Access Journals (Sweden)
Rui Wang
2014-01-01
Full Text Available A modified multiple structural changes model is built to test structural breaks of the financial system based on calculating the largest Lyapunov exponents of the financial time series. Afterwards, the Lorenz system is used as a simulation example to inspect the new model. As the Lorenz system has strong nonlinearity, the verification results show that the new model has good capability in both finding the breakpoint and revealing the changes in nonlinear characteristics of the time series. The empirical study based on the model used daily data from the S&P 500 stock index during the global financial crisis from 2005 to 2012. The results provide four breakpoints of the period, which divide the contagion into four stages: stationary, local outbreak, global outbreak, and recovery period. An additional significant result is the obvious chaos characteristic difference in the largest Lyapunov exponents and the standard deviation at various stages, particularly at the local outbreak stage.
Zeren, Tamer; Özbek, Mustafa; Kutlu, Necip; Akilli, Mahmut
2016-01-05
Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of systems such as the cardiorespiratory system. In this study, we recorded tracheal air flow signals, including PNCG signals, from 3 representative anesthetized rats and analyzed the nonlinear behavior of these complex signals using Lyapunov exponents. Lyapunov exponents may also be used to determine the normal and pathological structure of biological systems. If the signals have at least one positive Lyapunov exponent, the signals reflect chaotic activity, as seen in PNCG signals in rats; the largest Lyapunov exponents of the signals of the healthy rats were greater than zero in this study. A method was proposed to determine the diagnostic and prognostic values of the cardiorespiratory system of rats using the arrangement of the PNCG and Lyapunov exponents, which may be monitored as vitality indicators.
Coordinate-invariant incremental Lyapunov functions
Zamani, Majid
2011-01-01
The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. In this type of stability, the focus is on the convergence of trajectories with respect to themselves, rather than with respect to an equilibrium point or a particular trajectory. Similarly to stability, Lyapunov functions play an important role in the study of incremental stability. In this paper, we propose coordinate-invariant notions of incremental Lyapunov function and provide the description of incremental stability in terms of existence of the proposed Lyapunov functions. Moreover, we develop a backstepping design approach providing a recursive way of constructing controllers as well as incremental Lyapunov functions. The effectiveness of our method is illustrated by synthesizing a controller rendering a single-machine infinite-bus electrical power system incrementally stable.
Robust lyapunov controller for uncertain systems
Laleg-Kirati, Taous-Meriem
2017-02-23
Various examples of systems and methods are provided for Lyapunov control for uncertain systems. In one example, a system includes a process plant and a robust Lyapunov controller configured to control an input of the process plant. The robust Lyapunov controller includes an inner closed loop Lyapunov controller and an outer closed loop error stabilizer. In another example, a method includes monitoring a system output of a process plant; generating an estimated system control input based upon a defined output reference; generating a system control input using the estimated system control input and a compensation term; and adjusting the process plant based upon the system control input to force the system output to track the defined output reference. An inner closed loop Lyapunov controller can generate the estimated system control input and an outer closed loop error stabilizer can generate the system control input.
Stability Analysis of Grasps with a Robotic Multifingered Hand
Institute of Scientific and Technical Information of China (English)
WAN An-hua
2005-01-01
Stability is a significant property for a robot hand grasp to perform complex tasks similar to human hands. The common method to investigate the stability of robotic multi-fingered grasp system is Lyapunov direct method, but usually it is rather difficult to construct a proper Lyapunov function. Avoiding the hard work of constructing a Lyapunov function, we propose the sufficient conditions for stability of the robotic grasp system.
MIMO Lyapunov Theory-Based RBF Neural Classifier for Traffic Sign Recognition
Directory of Open Access Journals (Sweden)
King Hann Lim
2012-01-01
Full Text Available Lyapunov theory-based radial basis function neural network (RBFNN is developed for traffic sign recognition in this paper to perform multiple inputs multiple outputs (MIMO classification. Multidimensional input is inserted into RBF nodes and these nodes are linked with multiple weights. An iterative weight adaptation scheme is hence designed with regards to the Lyapunov stability theory to obtain a set of optimum weights. In the design, the Lyapunov function has to be well selected to construct an energy space with a single global minimum. Weight gain is formed later to obey the Lyapunov stability theory. Detail analysis and discussion on the proposed classifier’s properties are included in the paper. The performance comparisons between the proposed classifier and some existing conventional techniques are evaluated using traffic sign patterns. Simulation results reveal that our proposed system achieved better performance with lower number of training iterations.
Random Matrices and Lyapunov Coefficients Regularity
Gallavotti, Giovanni
2017-02-01
Analyticity and other properties of the largest or smallest Lyapunov exponent of a product of real matrices with a "cone property" are studied as functions of the matrices entries, as long as they vary without destroying the cone property. The result is applied to stability directions, Lyapunov coefficients and Lyapunov exponents of a class of products of random matrices and to dynamical systems. The results are not new and the method is the main point of this work: it is is based on the classical theory of the Mayer series in Statistical Mechanics of rarefied gases.
Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. These results are also extended to autonomous switched systems subject to polytopic uncertainty. Furthermore, the proposed stability theorems are reformulated using the sum of squares decomposition method...... which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques....
Upper quantum Lyapunov exponent and parametric oscillators
Jauslin, H. R.; Sapin, O.; Guérin, S.; Wreszinski, W. F.
2004-11-01
We introduce a definition of upper Lyapunov exponent for quantum systems in the Heisenberg representation, and apply it to parametric quantum oscillators. We provide a simple proof that the upper quantum Lyapunov exponent ranges from zero to a positive value, as the parameters range from the classical system's region of stability to the instability region. It is also proved that in the instability region the parametric quantum oscillator satisfies the discrete quantum Anosov relations defined by Emch, Narnhofer, Sewell, and Thirring.
Kolyada, Sergiy; Rybak, Oleksandr
2013-01-01
We introduce and study the Lyapunov numbers -- quantitative measures of the sensitivity of a dynamical system $(X,f)$ given by a compact metric space $X$ and a continuous map $f:X \\to X$. In particular, we prove that for a minimal topologically weakly mixing system all Lyapunov numbers are the same.
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
A Converse Sum of Squares Lyapunov Result with a Degree Bound
Peet, Matthew M
2012-01-01
Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector field on a bounded set implies the existence of a Lyapunov function which is a sum-of-squares of polynomials. In particular, the main result states that if a system is exponentially stable on a bounded nonempty set, then there exists an SOS Lyapunov function which is exponentially decreasing on that bounded set. The proof is constructive and uses the Picard iteration. A bound on the degree of this converse Lyapunov function is also given. This result implies that semidefinite programming can be used to answer the question of stability of a polynomial vector field with a bound on complexity.
Circular orbit spacecraft control at the L4 point using Lyapunov functions
Agrawal, Rachana
2015-01-01
The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body problem (CRTBP). Incorporating the requirements of a fixed radius orbit and a desired angular momentum, a Lyapunov function is constructed and the requisite analysis is performed to obtain a controller. Asymptotic stability is proved in a defined region around the L4 point using LaSalle's principle.
Lyapunov function and the basin of attraction for a single-joint muscle-skeletal model.
Giesl, Peter; Wagner, Heiko
2007-04-01
This paper provides an explicit Lyapunov function for a general single-joint muscle-skeletal model. Using this Lyapunov function one can determine analytically large subsets of the basin of attraction of an asymptotically stable equilibrium. Besides providing an analytical tool for the analysis of such a system we consider an elbow model and show that the theoretical predictions are in agreement with experimental results. Moreover, we can thus distinguish between regions where the self-stabilizing properties of the muscle-skeletal system guarantee stability and regions where nerval control and reflexes are necessary.
Directory of Open Access Journals (Sweden)
Chuangxia Huang
2009-01-01
Full Text Available This paper is concerned with pth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. With the help of Lyapunov method, stochastic analysis, and inequality techniques, a set of new suffcient conditions on pth moment exponential stability for the considered system is presented. The proposed results generalized and improved some earlier publications.
Institute of Scientific and Technical Information of China (English)
S. Lakshmanan; P. Balasubramaniarn
2011-01-01
This paper studies the problem of linear matrix inequality(LMI)approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.
Comparison between covariant and orthogonal Lyapunov vectors.
Yang, Hong-liu; Radons, Günter
2010-10-01
Two sets of vectors, covariant Lyapunov vectors (CLVs) and orthogonal Lyapunov vectors (OLVs), are currently used to characterize the linear stability of chaotic systems. A comparison is made to show their similarity and difference, especially with respect to the influence on hydrodynamic Lyapunov modes (HLMs). Our numerical simulations show that in both Hamiltonian and dissipative systems HLMs formerly detected via OLVs survive if CLVs are used instead. Moreover, the previous classification of two universality classes works for CLVs as well, i.e., the dispersion relation is linear for Hamiltonian systems and quadratic for dissipative systems, respectively. The significance of HLMs changes in different ways for Hamiltonian and dissipative systems with the replacement of OLVs with CLVs. For general dissipative systems with nonhyperbolic dynamics the long-wavelength structure in Lyapunov vectors corresponding to near-zero Lyapunov exponents is strongly reduced if CLVs are used instead, whereas for highly hyperbolic dissipative systems the significance of HLMs is nearly identical for CLVs and OLVs. In contrast the HLM significance of Hamiltonian systems is always comparable for CLVs and OLVs irrespective of hyperbolicity. We also find that in Hamiltonian systems different symmetry relations between conjugate pairs are observed for CLVs and OLVs. Especially, CLVs in a conjugate pair are statistically indistinguishable in consequence of the microreversibility of Hamiltonian systems. Transformation properties of Lyapunov exponents, CLVs, and hyperbolicity under changes of coordinate are discussed in appendices.
Stability Analysis of Neural Networks-Based System Identification
Directory of Open Access Journals (Sweden)
Talel Korkobi
2008-01-01
Full Text Available This paper treats some problems related to nonlinear systems identification. A stability analysis neural network model for identifying nonlinear dynamic systems is presented. A constrained adaptive stable backpropagation updating law is presented and used in the proposed identification approach. The proposed backpropagation training algorithm is modified to obtain an adaptive learning rate guarantying convergence stability. The proposed learning rule is the backpropagation algorithm under the condition that the learning rate belongs to a specified range defining the stability domain. Satisfying such condition, unstable phenomena during the learning process are avoided. A Lyapunov analysis leads to the computation of the expression of a convenient adaptive learning rate verifying the convergence stability criteria. Finally, the elaborated training algorithm is applied in several simulations. The results confirm the effectiveness of the CSBP algorithm.
Stability Analysis for Stochastic Delayed High-order Neural Networks
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with time-delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibrium point in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities (LMIs). Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow
Vastano, John A.; Moser, Robert D.
1991-01-01
The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow
Vastano, John A.; Moser, Robert D.
1991-01-01
The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.
Biased random walks, lyapunov functions, and stochastic analysis of best fit bin packing
Energy Technology Data Exchange (ETDEWEB)
Kenyon, C. [CNRS, Lyon (France); Rabani, Y. [Technion, Haifa (Israel); Sinclair, A. [Univ. of California, Berkeley, CA (United States)
1996-12-31
We study the average case performance of the Best Fit algorithm for on-line bin packing under the distribution U(j,k), in which the item sizes are uniformly distributed in the discrete range (1/k, 2/k,..., j/k). Our main result is that, in the case j = k - 2, the expected waste for an infinite stream of items remains bounded. This settles an open problem posed recently by Coffman et al. It is also the first result which involves a detailed analysis of the infinite multi-dimensional Markov chain underlying the algorithm.
Construction of Lyapunov functions by the localization method
Krishchenko, A. P.; Kanatnikov, A. N.
2017-07-01
In this paper, we examine the problem of construction of Lyapunov functions for asymptotically stable equilibrium points. We exploit conditions of asymptotic stability in terms of compact invariant sets and positively invariant sets. Our results are methods of verification of these conditions and construction of Lyapunov functions by the localization method of compact invariant sets. These results are illustrated by an example.
Mizuta, Keisuke; Tokita, Takashi; Ito, Yatsuji; Aoki, Mitsuhiro; Kuze, Bunya
2009-12-01
largest Lyapunov exponents has a different significance from instability of standing posture indicated by a conventional analysis. We propose that the largest Lyapunov exponents may be an useful subsidiary measure to evaluate postural stability and its change due to vestibular dysfunction.
Improved Stability Analysis of Nonlinear Networked Control Systems over Multiple Communication Links
Delavar, Rahim; Tavassoli, Babak; Beheshti, Mohammad Taghi Hamidi
2015-01-01
In this paper, we consider a nonlinear networked control system (NCS) in which controllers, sensors and actuators are connected via several communication links. In each link, networking effects such as the transmission delay, packet loss, sampling jitter and data packet miss-ordering are captured by time-varying delays. Stability analysis is carried out based on the Lyapunov Krasovskii method to obtain a condition for stability of the nonlinear NCS in the form of linear matrix inequality (LMI...
Lyapunov functions for fractional order systems
Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A.; Gallegos, Javier A.
2014-09-01
A new lemma for the Caputo fractional derivatives, when 0<α<1, is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
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Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Multiple integral inequalities and stability analysis of time delay systems
Gyurkovics, Eva; Takacs, Tibor
2016-01-01
This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen's and Wirtinger's inequalities, as well as the recently presented Bessel-Legendre inequalities of A. Seuret and F. Gouaisbaut, (2015) and the Wirtinger-based multiple-integral inequalities of M. Park et al. (2015) and T.H. Lee et al. (2015). The present paper aims at showing that the propos...
Directory of Open Access Journals (Sweden)
M. Widi Triyatno
2015-03-01
Full Text Available Disturbances in the operation of the power system may cause disturbance in voltage stability. Therefore, dynamic voltage stability analysis before and after disturbance needs to be performed. This paper proposes dynamic voltage stability prediction using maximum Lyapunov exponent with Lampung’s electrical system as case study. Voltage stability simulation is performed with various types of disturbances that occur at line between of Baturaja substation and Bukit Kemuning substation. Time-series data of voltage measurement of simulation results at GI Baturaja is applied for voltage stability prediction analysis using maximum Lyapunov exponent. With the same number of data samples and the same time for circuit breakers to interrupt disturbances, the simulation results using maximum Lyapunov exponent show that the voltage can be stabilized at 1.7 seconds after the occurrence of the three-phase disturbance, at 1.2 seconds after the occurrence of the phase-to-ground disturbance, at 0,9 second after the occurrence of the disturbance between phase, at 1.2 seconds after the occurrence of the loss of line disturbance and 1.4 seconds after the occurrence of the loss of load disturbance. The amount of data samples used in analysis affect the time for the voltage reaches stability.
Stability Analysis on Speed Control System of Autonomous Underwater Vehicle
Institute of Scientific and Technical Information of China (English)
LI Ye; PANG Yong-jie; WAN Lei; WANG Fang; LIAO Yu-lei
2009-01-01
The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle (AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov' s direct method is proposed in this paper.After decoupling the six degree-of-freedom (DOF) motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.
Stability Analysis of a Microgrid System based on Inverter-Interfaced Distributed Generators
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CUSIDO, J.
2013-08-01
Full Text Available This paper presents a phase-plane trajectory analysis and the appliance of Lyapunov's methodology to evaluate the stability limits of a small signal model of a Microgrid system. The work done is based on a non-linear tool and several computer simulations. The study indicates how to analyze a Microgrid system that is subjected to a severe transient disturbance by using its large signal model without the necessity of the small signal analysis as it is commonly applied.
Robinett III, Rush D
2011-01-01
Nonlinear Powerflow Control Design presents an innovative control system design process motivated by renewable energy electric grid integration problems. The concepts developed result from the convergence of three research and development goals: • to create a unifying metric to compare the value of different energy sources – coal-burning power plant, wind turbines, solar photovoltaics, etc. – to be integrated into the electric power grid and to replace the typical metric of costs/profit; • to develop a new nonlinear control tool that applies power flow control, thermodynamics, and complex adaptive systems theory to the energy grid in a consistent way; and • to apply collective robotics theories to the creation of high-performance teams of people and key individuals in order to account for human factors in controlling and selling power into a distributed, decentralized electric power grid. All three of these goals have important concepts in common: exergy flow, limit cycles, and balance between compe...
An application of lyapunov stability analysis to improve\\ud the performance of NARMAX models
Akanyeti, O.; Rano, I.; Nehmzow, U.; S. A. Billings
2009-01-01
Previously we presented a novel approach to program a robot controller based on system identification and robot training techniques. The proposed method works in two stages: first, the programmer demonstrates the desired behaviour to the robot by driving it manually in the target environment. During this run, the sensory perception and the desired velocity commands of the robot are logged. Having thus obtained training data we model the relationship between sensory readings and the motor comm...
Fuzzy Lyapunov Reinforcement Learning for Non Linear Systems.
Kumar, Abhishek; Sharma, Rajneesh
2017-03-01
We propose a fuzzy reinforcement learning (RL) based controller that generates a stable control action by lyapunov constraining fuzzy linguistic rules. In particular, we attempt at lyapunov constraining the consequent part of fuzzy rules in a fuzzy RL setup. Ours is a first attempt at designing a linguistic RL controller with lyapunov constrained fuzzy consequents to progressively learn a stable optimal policy. The proposed controller does not need system model or desired response and can effectively handle disturbances in continuous state-action space problems. Proposed controller has been employed on the benchmark Inverted Pendulum (IP) and Rotational/Translational Proof-Mass Actuator (RTAC) control problems (with and without disturbances). Simulation results and comparison against a) baseline fuzzy Q learning, b) Lyapunov theory based Actor-Critic, and c) Lyapunov theory based Markov game controller, elucidate stability and viability of the proposed control scheme.
Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian
2000-01-01
of the Lyapunov matrix equation and characterize the set of matrices $(B, C)$ which guarantees marginal stability. The theory is applied to gyroscopic systems, to indefinite damped systems, and to circulatory systems, showing how to choose certain parameter matrices to get sufficient conditions for marginal...
Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems
Liu, Jiang; Zhao, Hengjun
2011-01-01
The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard Lyapunov functions to relaxed Lyapunov functions (RLFs), by considering higher order Lie derivatives of certain functions along the system's vector field. Furthermore, we present a complete method to automatically discovering polynomial RLFs for polynomial dynamical systems (PDSs). Our method is complete in the sense that it is able to discover all polynomial RLFs by enumerating all polynomial templates for any PDS.
Institute of Scientific and Technical Information of China (English)
吴东平
2012-01-01
基于Lyapunov运动稳定性理论,经过推导可知,一个单自由度的某一个受迫振动的特解的运动稳定性问题等价于这个单自由度系统自由振动的稳定问题.对于复杂非线性系统的动力稳定性问题,直接应用Lyapunov理论进行系统的动力稳定性判定比较困难,考虑大跨度拱型结构的变形特征,提出一种简洁、实用且适合数值计算的动力稳定性判别方法——位移时程变化法.运用该方法计算结构在承受一般动荷载类型和不同计算条件下的动力稳定性,验证此方法的实用性及正确性.%Based on the stability theory of Lyapunov motion,it can be derived that the motion stability problem of a particular solution to a forced vibration of a single degree of freedom system,is equal to the stability problem of the free vibration system of single degree of freedom.For a dynamic stability problem of complex nonlinear system,it is difficult to judge the dynamic stability of a system by the theory of Lyapunov motion directly.Considering the deformation feature of a large-span arch structure,a simple and practical theory named deformation history theory which is suitable for digital computation to judge the dynamic stability of an arch structure is put forward and used to judge the dynamic stability of an arch structure under common dynamic loading and different conditions.It is shown that the theory is applicable and reasonable.
Stability Analysis and H∞ Output Tracking Control for Linear Systems with Time-Varying Delays
Directory of Open Access Journals (Sweden)
K. H. Kim
2014-01-01
Full Text Available The problem of stability analysis and H∞ output tracking control for linear systems with time-varying delays is studied. First, by construction of a newly augmented Lyapunov-Krasovskii functional, a delay-dependent stability criterion for nominal systems with time-varying delays is established in terms of linear matrix inequalities (LMIs. Second, based on the H∞ sense, the proposed method is extended to solve the problem of designing an H∞ output tracking controller to track the output of a given reference model. Finally, three examples are included to show the validity and effectiveness of the presented delay-dependent stability and the H∞ output tracking controller design.
Stability Analysis for Recurrent Neural Networks with Time-varying Delay
Institute of Scientific and Technical Information of China (English)
Yuan-Yuan Wu; Yu-Qiang Wu
2009-01-01
This paper is concerned with the stability analysis for static recurrent neural networks (RNNs) with time-varying delay. By Lyapunov functional method and linear matrix inequality technique, some new delay-dependent conditions are established to ensure the asymptotic stability of the neural network. Expressed in linear matrix inequalities (LMIs), the proposed delay-dependent stability conditions can be checked using the recently developed algorithms. A numerical example is given to show that the obtained conditions can provide less conservative results than some existing ones.
Stability analysis of discrete-time BAM neural networks based on standard neural network models
Institute of Scientific and Technical Information of China (English)
ZHANG Sen-lin; LIU Mei-qin
2005-01-01
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
Lyapunov Computational Method for Two-Dimensional Boussinesq Equation
Mabrouk, Anouar Ben
2010-01-01
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.
Lyapunov functions for a class of nonlinear systems using Caputo derivative
Fernandez-Anaya, G.; Nava-Antonio, G.; Jamous-Galante, J.; Muñoz-Vega, R.; Hernández-Martínez, E. G.
2017-02-01
This paper presents an extension of recent results that allow proving the stability of Caputo nonlinear and time-varying systems, by means of the fractional order Lyapunov direct method, using quadratic Lyapunov functions. This article introduces a new way of building polynomial Lyapunov functions of any positive integer order as a way of determining the stability of a greater variety of systems when the order of the derivative is 0 < α < 1. Some examples are given to validate these results.
A unified perspective on robot control - The energy Lyapunov function approach
Wen, John T.
1990-01-01
A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.
Jumping property of Lyapunov values
Institute of Scientific and Technical Information of China (English)
毛锐; 王铎
1996-01-01
A sufficient condition for fcth Lyapunov value to be zero for planar polynomial vector fields is given, which extends the result of "jumping property’ of Lyapunov values obtained by Wang Duo to more general cases. A concrete example that the origin cannot be weak focus of order 1, 2, 4, 5, 8 is presented.
Branicki, Michal
2009-01-01
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of "transport barriers" in the flow, i.e. material curves and surfaces. We argue that a general theory of Lagrangian transport has to account for the effects of transient flow phenomena which are not captured by the infinite-time notions of hyperbolicity even for flows defined for all time. Notions of finite-time hyperbolic trajectories, their finite time stable and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE) fields and associated Lagra...
Stability analysis of ferrofluids
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Katharina Duda
2015-09-01
Full Text Available Superparamagnetic iron oxides (SPIOs are used as tracer for the new imaging technique Magnetic Particle Imaging. The stability of ferrofluids for medical application has a great importance, in addition to the particle size. The shell material, which protects the iron core prior from agglomeration and sedimentation, can be degraded by various processes. Another important aspect of stability is the constant performance of magnetisation. Therefore, the measurement of the magnetisation of the particles must be controlled in order to ensure the stability of the samples.
Time-Delay Systems Lyapunov Functionals and Matrices
Kharitonov, Vladimir L
2013-01-01
Stability is one of the most studied issues in the theory of time-delay systems, but the corresponding chapters of published volumes on time-delay systems do not include a comprehensive study of a counterpart of classical Lyapunov theory for linear delay free systems. The principal goal of the book is to fill this gap, and to provide readers with a systematic and exhaustive treatment of the basic concepts of the Lyapunov-Krasovskii approach to the stability analysis of linear time-delay systems. The book is organized into two parts. The first part is dedicated to the case of retarded type time-delay systems; it consists of four chapters, which respectively deal with results concerning the existence and uniqueness of the solutions of an initial value problem, the class of linear systems with one delay, the case of systems with several delays, and the case of systems with distributed delays. The second part of the book studies the case of neutral type time-delay systems, containing three chapters that e...
Universal construction of control Lyapunov functions for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically.Based on the control Lyapunov function,a feedback control is obtained to stabilize the closed-loop system.In addition,this method is applied to stabilize the Benchmark system.A simulation shows the effectiveness of the method.
Directory of Open Access Journals (Sweden)
M. Branicki
2010-01-01
Full Text Available We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of transport barriers in the flow, i.e. material curves and surfaces. We argue that a general theory of Lagrangian transport has to account for the effects of transient flow phenomena which are not captured by the infinite-time notions of hyperbolicity even for flows defined for all time. Notions of finite-time hyperbolic trajectories, their finite time stable and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE fields and associated Lagrangian coherent structures have been the main tools for characterising transport barriers in the time-aperiodic situation. In this paper we consider a variety of examples, some with explicit solutions, that illustrate in a concrete manner the issues and phenomena that arise in the setting of finite-time dynamical systems. Of particular significance for geophysical applications is the notion of flow transition which occurs when finite-time hyperbolicity is lost or gained. The phenomena discovered and analysed in our examples point the way to a variety of directions for rigorous mathematical research in this rapidly developing and important area of dynamical systems theory.
Stability and bifurcation analysis of a vector-bias model of malaria transmission.
Buonomo, Bruno; Vargas-De-León, Cruz
2013-03-01
The vector-bias model of malaria transmission, recently proposed by Chamchod and Britton, is considered. Nonlinear stability analysis is performed by means of the Lyapunov theory and the LaSalle Invariance Principle. The classical threshold for the basic reproductive number, R(0), is obtained: if R(0)>1, then the disease will spread and persist within its host population. If R(0)1, the endemic persistence of the disease has been proved to hold also for the extended model. This last result is obtained by means of the geometric approach to global stability. Copyright © 2012 Elsevier Inc. All rights reserved.
Robust Stability Analysis and Synthesis for Switched Discrete-Time Systems with Time Delay
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Liguo Zhang
2010-01-01
Full Text Available The problems of robust stability analysis and synthesis for a class of uncertain switched time-delay systems with polytopic type uncertainties are addressed. Based on the constructive use of an appropriate switched Lyapunov function, sufficient linear matrix inequalities (LMIs conditions are investigated to make such systems a uniform quadratic stability with an L2-gain smaller than a given constant level. System synthesis is to design switched feedback schemes, whether based on state, output measurements, or by using dynamic output feedback, to guarantee that the corresponding closed-loop system satisfies the LMIs conditions. Two numerical examples are provided that demonstrate the efficiency of this approach.
Global Stability Analysis for an Internet Congestion Control Model with a Time-Varying Link Capacity
Rezaie, B; Analoui, M; Khorsandi, S
2009-01-01
In this paper, a global stability analysis is given for a rate-based congestion control system modeled by a nonlinear delayed differential equation. The model determines the dynamics of a single-source single-link network, with a time-varying capacity of link and a fixed communication delay. We obtain a sufficient delay-independent conditions on system parameters under which global asymptotic stability of the system is guarantied. The proof is based on an extension of Lyapunov-Krasovskii theorem for a class of nonlinear time-delay systems. The numerical simulations for a typical scenario justify the theoretical results.
Stability analysis of delayed neural networks via a new integral inequality.
Yang, Bin; Wang, Juan; Wang, Jun
2017-04-01
This paper focuses on stability analysis for neural networks systems with time-varying delays. A more general auxiliary function-based integral inequality is established and some improved delay-dependent stability conditions formulated in terms of linear matrix inequalities (LMIs) are derived by employing a suitable Lyapunov-Krasovskii functional (LKF) and the novel integral inequality. Three well-known application examples are provided to demonstrate the effectiveness and improvements of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.
Analysis of stability boundaries of satellite's equilibrium attitude in a circular orbit
Novikov, M. A.
2016-03-01
An asymmetric satellite equipped with control momentum gyroscopes (CMGs) with the center of mass of the system moving uniformly in a circular orbit was considered. The stability of a relative equilibrium attitude of the satellite was analyzed using Lyapunov's direct method. The Lyapunov function V is a positive definite integral of the total energy of the perturbed motion of the system. The asymptotic stability analysis of the stationary motion of the conservative system was based on the Barbashin-Krasovskii theorem on the nonexistence of integer trajectories of the set dot V, which was obtained using the differential equations of motion of the satellite with CMGs. By analyzing the sign definiteness of the quadratic part of V, it was found earlier by V.V. Sazonov that the stability region is described by four strict inequalities. The asymptotic stability at the stability boundary was analyzed by sequentially turning these inequalities into equalities with terms of orders higher than the second taken into account in V. The sign definiteness analysis of the inhomogeneous function V at the stability boundary involved a huge amount of computations related to the multiplication, expansion, substitution, and factorization of symbolic expressions. The computations were performed by applying a computer algebra system on a personal computer.
Lyapunov modes in extended systems.
Yang, Hong-Liu; Radons, Günter
2009-08-28
Hydrodynamic Lyapunov modes, which have recently been observed in many extended systems with translational symmetry, such as hard sphere systems, dynamic XY models or Lennard-Jones fluids, are nowadays regarded as fundamental objects connecting nonlinear dynamics and statistical physics. We review here our recent results on Lyapunov modes in extended system. The solution to one of the puzzles, the appearance of good and 'vague' modes, is presented for the model system of coupled map lattices. The structural properties of these modes are related to the phase space geometry, especially the angles between Oseledec subspaces, and to fluctuations of local Lyapunov exponents. In this context, we report also on the possible appearance of branches splitting in the Lyapunov spectra of diatomic systems, similar to acoustic and optical branches for phonons. The final part is devoted to the hyperbolicity of partial differential equations and the effective degrees of freedom of such infinite-dimensional systems.
Lyapunov decay in quantum irreversibility.
García-Mata, Ignacio; Roncaglia, Augusto J; Wisniacki, Diego A
2016-06-13
The Loschmidt echo--also known as fidelity--is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is carried out. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as has been shown for quantum maps. In this work, we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime.
Controller design for TS models using delayed nonquadratic Lyapunov functions.
Lendek, Zsofia; Guerra, Thierry-Marie; Lauber, Jimmy
2015-03-01
In the last few years, nonquadratic Lyapunov functions have been more and more frequently used in the analysis and controller design for Takagi-Sugeno fuzzy models. In this paper, we developed relaxed conditions for controller design using nonquadratic Lyapunov functions and delayed controllers and give a general framework for the use of such Lyapunov functions. The two controller design methods developed in this framework outperform and generalize current state-of-the-art methods. The proposed methods are extended to robust and H∞ control and α -sample variation.
Stability Analysis of Uncertain Discrete Time-Delay Control Systems
Institute of Scientific and Technical Information of China (English)
Long Xuming; Duan Ping
2006-01-01
Based on Lyapunov stability theory, a less conservative sufficient conditions for the stabilities of uncertain discrete delay-independent and delay-dependent control systems are obtained by using the linear matrix inequality (LMI) approach. Judgement of the stability of time-delay systems is transformed to judgement of the feasible solution of an LMI, and hence is solved by use of MATLAB. Numerical simulations verify the validity of the proposed method.
Using Lyapunov exponents to predict the onset of chaos in nonlinear oscillators.
Ryabov, Vladimir B
2002-07-01
An analytic technique for predicting the emergence of chaotic instability in nonlinear nonautonomous dissipative oscillators is proposed. The method is based on the Lyapunov-type stability analysis of an arbitrary phase trajectory and the standard procedure of calculating the Lyapunov characteristic exponents. The concept of temporally local Lyapunov exponents is then utilized for specifying the area in the phase space where any trajectory is asymptotically stable, and, therefore, the existence of chaotic attractors is impossible. The procedure of linear coordinate transform optimizing the linear part of the vector field is developed for the purpose of maximizing the stability area in the vicinity of a stable fixed point. By considering the inverse conditions of asymptotic stability, this approach allows formulating a necessary condition for chaotic motion in a broad class of nonlinear oscillatory systems, including many cases of practical interest. The examples of externally excited one- and two-well Duffing oscillators and a planar pendulum demonstrate efficiency of the proposed method, as well as a good agreement of the theoretical predictions with the results of numerical experiments. The comparison of the proposed method with Melnikov's criterion shows a potential advantage of using the former one at high values of dissipation parameter and/or multifrequency type of excitation in dynamical systems.
Nonlinear Direct Robust Adaptive Control Using Lyapunov Method
Directory of Open Access Journals (Sweden)
Chunbo Xiu
2013-07-01
Full Text Available The problem of robust adaptive stabilization of a class of multi-input nonlinear systems with arbitrary unknown parameters and unknown structure of bounded variation have been considered. By employing the direct adaptive and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the system states. By employing our result, a kind of nonlinear system is analyzed, the concrete form of the control law is given and the meaningful quadratic control Lyapunov function for the system is constructed. Simulation of parallel manipulator is provided to illustrate the effectiveness of the proposed method.
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability analysis of impulsive functional systems of fractional order
Stamova, Ivanka; Stamov, Gani
2014-03-01
In this paper, a class of impulsive fractional functional differential systems is investigated. Sufficient conditions for stability of the zero solution are proved, extending the corresponding theory of impulsive functional differential equations. The investigations are carried out by using the comparison principle, coupled with the Lyapunov function method. We apply our results to an impulsive single species model of Lotka-Volterra type.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
The direct Lyapunov method for the stabilisation of the Furuta pendulum
Aguilar-Ibañez, Carlos; Suárez-Castañón, Miguel S.; Gutiérres-Frias, Oscar O.
2010-11-01
A nonlinear controller for the stabilisation of the Furuta pendulum is presented. The control strategy is based on a partial feedback linearisation. In a first stage only the actuated coordinate of the Furuta pendulum is linearised. Then, the stabilising feedback controller is obtained by applying the Lyapunov direct method. That is, using this method we prove local asymptotic stability and demonstrate that the closed-loop system has a large region of attraction. The stability analysis is carried out by means of LaSalle's invariance principle. To assess the controller effectiveness, the results of the corresponding numerical simulations are presented.
Robust stability analysis of uncertain discrete-time systems with state delay
Institute of Scientific and Technical Information of China (English)
任正云; 张立群; 邵惠鹤
2004-01-01
The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.
A variational approach to Lyapunov type inequalities from ODEs to PDEs
Cañada, Antonio
2015-01-01
This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and ...
Convex Optimization methods for computing the Lyapunov Exponent of matrices
Protasov, Vladimir Yu
2012-01-01
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for the Lyapunov exponent. They improve previously known bounds and converge to the real value. The rate of convergence is estimated and the efficiency of the algorithm is demonstrated on several problems from applications (in functional analysis, combinatorics, and lan- guage theory) and on numerical examples with randomly generated matrices. The method computes the Lyapunov exponent with a prescribed accuracy in relatively high dimensions (up to 60). We generalize this approach to all matrices, not necessar- ily nonnegative, derive a new universal upper bound for the Lyapunov exponent, and show that such a lower bound, in general, does not exist.
STABILITY ANALYSIS OF A COMPUTER VIRUS PROPAGATION MODEL WITH ANTIDOTE IN VULNERABLE SYSTEM
Institute of Scientific and Technical Information of China (English)
Nguyen Huu KHANH; Nguyen Bich HUY
2016-01-01
We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold R0. If R0 ≤ 1, the virus-free equilibrium is globally asymptotically stable, and if R0 >1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Stability of melt crystal growth under microgravity conditions
Tatarchenko, V. A.
The conception of dynamic stability of melt crystal growth has been developed. The method based on the Lyapunov stability theory has been used to the study stability of crystallization by capillary shaping techniques including Czokhralsky, Stepanov, Kiropoulos, Verneuil and floating zone methods. Preliminary results of the stability analysis of crystallization by floating zone technique under microgravity conditions are presented here.
Slope Stability Analysis Using GIS
Bouajaj, Ahmed; Bahi, Lahcen; Ouadif, Latifa; Awa, Mohamed
2016-10-01
An analysis of slope stability using Geographic Information System (GIS) is presented in this paper. The methodology is based on the calculation of the safety factor in 2D and 3D using ArcGis. Hovland's Method in 3D and 2D were used in the stability analysis of the slope located at the 34 kilometer point (K.P.34) on the highway in the North of Morocco connecting Tangier to Ksar Sghir. Results shows that the safety factors obtained in 3D are always higher than those obtained in 2D and the slope becomes unstable when the water table level is less than 1 m.
SLOPE STABILITY ANALYSIS USING GIS
Directory of Open Access Journals (Sweden)
A. Bouajaj
2016-10-01
Full Text Available An analysis of slope stability using Geographic Information System (GIS is presented in this paper. The methodology is based on the calculation of the safety factor in 2D and 3D using ArcGis. Hovland's Method in 3D and 2D were used in the stability analysis of the slope located at the 34 kilometer point (K.P.34 on the highway in the North of Morocco connecting Tangier to Ksar Sghir. Results shows that the safety factors obtained in 3D are always higher than those obtained in 2D and the slope becomes unstable when the water table level is less than 1 m.
Entanglement production and Lyapunov exponents
Hackl, Lucas; Bianchi, Eugenio; Yokomizo, Nelson
2017-01-01
Squeezed vacua play a prominent role in quantum field theory in curved spacetime. Instabilities and resonances that arise from the coupling in the field to the background geometry, result in a large squeezing of the vacuum. In this talk, I discuss the relation between squeezing and Lyapunov exponents of the system. In particular, I derive a new formula for the rate of growth of the entanglement entropy expressed as the sum of the Lyapunov exponents. Examples of such a linear production regime can be found during inflation and in the preheating phase directly after inflation.
DEFF Research Database (Denmark)
Skjoldan, P.F.; Hansen, Morten Hartvig
2009-01-01
Structures with isotropic bladed rotors can be modally analyzed by eigenvalue analysis of time-invariant Coleman transformed equations of motion related to the inertial frame or by Floquet analysis of the periodic equations of motion. The Coleman transformation is here shown to be a special case ...
Integral expressions of Lyapunov exponents for autonomous ordinary differential systems
Institute of Scientific and Technical Information of China (English)
DAI XiongPing
2009-01-01
In the paper,the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space Rd,not necessarily compact,by Liaowise spectral theorems that give integral expressions of Lyapunov exponents.In the context of smooth linear skew-product flows with Polish driving systems,the results are still valid.This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.
Integral expressions of Lyapunov exponents for autonomous ordinary differential systems
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space Rd, not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.
Stability Analysis of Continuous-Time Fuzzy Large-Scale System
Institute of Scientific and Technical Information of China (English)
曾怡达; 张友刚; 肖建
2003-01-01
A continuous-time fuzzy large-scale system F consists of some interconnected Takagi-Sugeno fuzzy subsystems. Two sufficient conditions for the asymptotic stability of this system (namely, theorem 1 and theorem 2) are derived via a multiple Lyapunov function approach. In theorem 1, the information of membership functions of fuzzy rules should be known in order to analyze the stability of F. But in general this information is not easy to be acquired for their time-varying property. So theorem 2 is provided to judge the asymptotic stability of F, based on which there is no need to know the information of membership functions in stability analysis. Finally, a numerical example is given to show the utility of the method proposed in this paper.
Formation stability analysis of unmanned multi-vehicles under interconnection topologies
Yang, Aolei; Naeem, Wasif; Fei, Minrui
2015-04-01
In this paper, the overall formation stability of an unmanned multi-vehicle is mathematically presented under interconnection topologies. A novel definition of formation error is first given and followed by the proposed formation stability hypothesis. Based on this hypothesis, a unique extension-decomposition-aggregation scheme is then employed to support the stability analysis for the overall multi-vehicle formation under a mesh topology. It is proved that the overall formation control system consisting of N number of nonlinear vehicles is not only asymptotically stable, but also exponentially stable in the sense of Lyapunov within a neighbourhood of the desired formation. This technique is shown to be applicable for a mesh topology but is equally applicable for other topologies. A simulation study of the formation manoeuvre of multiple Aerosonde UAVs (unmanned aerial vehicles), in 3-D space, is finally carried out verifying the achieved formation stability result.
Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way.Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.
Parameter-dependent Lyapunov functional for systems with multiple time delays
Institute of Scientific and Technical Information of China (English)
Min WU; Yong HE
2004-01-01
The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties.The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional.The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between the terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices.In addition,the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived.Numerical examples demonstrate that the proposed criteria are more effective than the previous results.
Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization
Christiansen, F; Christiansen, Freddy; Rugh, Hans Henrik
1996-01-01
We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability parameter beta>0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt orthonormalized and at most linear growth of the dynamical variables is involved. We prove that the method is strongly stable when beta > -lambda_k where lambda_k is the k'th Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.
Directory of Open Access Journals (Sweden)
Zhixiong Zhong
2013-01-01
Full Text Available The stability analysis and stabilization of Takagi-Sugeno (T-S fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
Ipsen, J. R.; Schomerus, H.
2016-09-01
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May-Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for a more detailed analysis of the stability-instability phase transition. Our derivations rest on an explicit formulation of a Fokker-Planck equation for the Lyapunov exponents. This formulation happens to coincide with an exactly solvable class of models of the Calgero-Sutherland type, originally encountered for a model of phase-coherent transport. The exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices, and is also closely related to Hermitian matrix models with an external source.
Universal scaling of Lyapunov-exponent fluctuations in space-time chaos.
Pazó, Diego; López, Juan M; Politi, Antonio
2013-06-01
Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase space. A recent numerical study of spatially extended systems has revealed that the diffusion coefficient D of the Lyapunov exponents (LEs) exhibits a nontrivial scaling behavior, D(L)~L(-γ), with the system size L. Here, we show that the wandering exponent γ can be expressed in terms of the roughening exponents associated with the corresponding "Lyapunov surface." Our theoretical predictions are supported by the numerical analysis of several spatially extended systems. In particular, we find that the wandering exponent of the first LE is universal: in view of the known relationship with the Kardar-Parisi-Zhang equation, γ can be expressed in terms of known critical exponents. Furthermore, our simulations reveal that the bulk of the spectrum exhibits a clearly different behavior and suggest that it belongs to a possibly unique universality class, which has, however, yet to be identified.
Institute of Scientific and Technical Information of China (English)
Wang Jia; Hui Guo-Tao; Xie Xiang-Peng
2013-01-01
We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional (2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded (polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.
Baire classes of Lyapunov invariants
Bykov, V. V.
2017-05-01
It is shown that no relations exist (apart from inherent ones) between Baire classes of Lyapunov transformation invariants in the compact- open and uniform topologies on the space of linear differential systems. It is established that if a functional on the space of linear differential systems with the compact-open topology is the repeated limit of a multisequence of continuous functionals, then these can be chosen to be determined by the values of system coefficients on a finite interval of the half-line (one for each functional). It is proved that the Lyapunov exponents cannot be represented as the limit of a sequence of (not necessarily continuous) functionals such that each of these depends only on the restriction of the system to a finite interval of the half-line. Bibliography: 28 titles.
Lyapunov Stability of Complementarity and Extended Systems
Camlibel, M. Kanat; Pang, Jong-Shi; Shen, Jinglai
2006-01-01
A linear complementarity system (LCS) is a piecewise linear dynamical system consisting of a linear time-invariant ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution to a finite-dimensional linear complementarity problem (LCP), whose
Stability Analysis of Ecomorphodynamic Equations
Bärenbold, Fabian; Perona, Paolo
2014-01-01
Although riparian vegetation is present in or along many water courses of the world, its active role resulting from the interaction with flow and sediment processes has only recently become an active field of research. Especially, the role of vegetation in the process of river pattern formation has been explored and demonstrated mostly experimentally and numerically until now. In the present work, we shed light on this subject by performing a linear stability analysis on a simple model for riverbed vegetation dynamics coupled with the set of classical river morphodynamic equations. The vegetation model only accounts for logistic growth, local positive feedback through seeding and resprouting, and mortality by means of uprooting through flow shear stress. Due to the simplicity of the model, we can transform the set of equations into an eigenvalue problem and assess the stability of the linearized equations when slightly perturbated away from a spatially homogeneous solution. If we couple vegetation dynamics wi...
Construction of Lyapunov Function for Dissipative Gyroscopic System
Institute of Scientific and Technical Information of China (English)
XU Wei; YUAN Bo; AO Ping
2011-01-01
@@ We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems.Such a potential function serves as the corresponding Lyapunov function for the dynamics,hence it gives both quantitative and qualitative descriptions for stability of motion.As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system.We explicitly obtain the potential function for all parameter regimes in the linear limit,including those regimes where the Lyapunov function was previously believed not to exist.%We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems. Such a potential function serves as the corresponding Lyapunov function for the dynamics, hence it gives both quantitative and qualitative descriptions for stability of motion. As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system. We explicitly obtain the potential function for all parameter regimes in the linear limit, including those regimes where the Lyapunov function was previously believed not to exist.
Lyapunov inequalities for the periodic boundary value problem at higher eigenvalues
Canada, Antonio
2009-01-01
This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the study of some special minimization problems, where the Lagrange multiplier Theorem plays a fundamental role. This allows to obtain the optimal constants. Our applications include the Hill's equation where we give some new conditions on its stability properties and also the study of periodic and nonlinear problems at resonance where we show some new conditions which allow to prove the existence and uniqueness of solutions.
Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators
Sicard, Pierre; Wen, John T.; Lanari, Leonardo
1992-01-01
A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward.
STABILITY ANALYSIS OF TWO-SECTORS STOCHASTIC ECONOMIC GROWTH MODEL
Institute of Scientific and Technical Information of China (English)
Shaobo ZHOU; Shigeng HU
2007-01-01
In the paper, we investigate the stability of a two-sector economic growth model under stochastic case. A two-dimensional stochastic differential system is deduced by Ito's formula, by using Lyapunov function methods, whether the growth rates of physical capital and human capital are exponentially stable or unstable depends on the values for parameters. Finally, we also illustrate the results with two examples.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
Directory of Open Access Journals (Sweden)
Bo Wang
2012-10-01
Full Text Available In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
Institute of Scientific and Technical Information of China (English)
M.Syed Ali
2012-01-01
This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi-Sugeno (T-S) model.The main results given here focus on the stability criteria using a new Lyapunov functional.New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature.Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.
Stability Criterion for Discrete-Time Systems
Directory of Open Access Journals (Sweden)
K. Ratchagit
2010-01-01
Full Text Available This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality.
Robust Backstepping Control Based on a Lyapunov Redesign for Skid-Steered Wheeled Mobile Robots
Directory of Open Access Journals (Sweden)
Eun-Ju Hwang
2013-01-01
Full Text Available This paper represents a robust backstepping tracking control based on a Lyapunov redesign for Skid‐Steered Wheeled Mobile Robots (WMRs. We present kinematic and dynamic models that explicitly relate the perturbations to the skidding in order to improve the tracking performance during real running. A robust controller is synthesized in the backstepping approach and the Lyapunov redesign technique, which forces the error dynamics to stabilize to the reference trajectories. We design an additional feedback control ‐ a Lyapunov redesign ‐ such that the overall control stabilizes the actual system in the presence of uncertainty and perturbation with the knowledge of the Lyapunov function. Simulation results are provided to validate and analyse the performance and stability of the proposed controller.
On Delay-independent Stability Criteria for Linear Time-delay Systems
Institute of Scientific and Technical Information of China (English)
Ai-Guo Wu; Guang-Ren Duan
2007-01-01
Several LMI representations for delay-independence stability are proposed by applying Projection Lemma and the socalled "Small Scalar Method". These criteria realize the elimination of the products coupling the system matrices and Lyapunov matrices by introducing some additional matrices. When they are applied to robust stability analysis for polytopic uncertain systems,the vertex-dependent Lyapunov functions are allowed, so less conservative results can be obtained. A numerical example is employed to illustrate the effect of these proposed criteria.
Liu, Pin-Lin
2015-07-01
This paper studies the problem of the stability analysis of interval time-varying delay systems with nonlinear perturbations. Based on the Lyapunov-Krasovskii functional (LKF), a sufficient delay-range-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI) and integral inequality approach (IIA) and delayed decomposition approach (DDA). Further, the delay range is divided into two equal segments for stability analysis. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Two well-known examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.
Lyapunov exponent in quantum mechanics A phase-space approach
Man'ko, V I
2000-01-01
Using the symplectic tomography map, both for the probability distributionsin classical phase space and for the Wigner functions of its quantumcounterpart, we discuss a notion of Lyapunov exponent for quantum dynamics.Because the marginal distributions, obtained by the tomography map, are alwayswell defined probabilities, the correspondence between classical and quantumnotions is very clear. Then we also obtain the corresponding expressions inHilbert space. Some examples are worked out. Classical and quantum exponentsare seen to coincide for local and non-local time-dependent quadraticpotentials. For non-quadratic potentials classical and quantum exponents aredifferent and some insight is obtained on the taming effect of quantummechanics on classical chaos. A detailed analysis is made for the standard map.Providing an unambiguous extension of the notion of Lyapunov exponent toquantum mechnics, the method that is developed is also computationallyefficient in obtaining analytical results for the Lyapunov expone...
Detecting Epileptic Seizure from Scalp EEG Using Lyapunov Spectrum
Directory of Open Access Journals (Sweden)
Truong Quang Dang Khoa
2012-01-01
Full Text Available One of the inherent weaknesses of the EEG signal processing is noises and artifacts. To overcome it, some methods for prediction of epilepsy recently reported in the literature are based on the evaluation of chaotic behavior of intracranial electroencephalographic (EEG recordings. These methods reduced noises, but they were hazardous to patients. In this study, we propose using Lyapunov spectrum to filter noise and detect epilepsy on scalp EEG signals only. We determined that the Lyapunov spectrum can be considered as the most expected method to evaluate chaotic behavior of scalp EEG recordings and to be robust within noises. Obtained results are compared to the independent component analysis (ICA and largest Lyapunov exponent. The results of detecting epilepsy are compared to diagnosis from medical doctors in case of typical general epilepsy.
Detecting epileptic seizure from scalp EEG using Lyapunov spectrum.
Khoa, Truong Quang Dang; Huong, Nguyen Thi Minh; Toi, Vo Van
2012-01-01
One of the inherent weaknesses of the EEG signal processing is noises and artifacts. To overcome it, some methods for prediction of epilepsy recently reported in the literature are based on the evaluation of chaotic behavior of intracranial electroencephalographic (EEG) recordings. These methods reduced noises, but they were hazardous to patients. In this study, we propose using Lyapunov spectrum to filter noise and detect epilepsy on scalp EEG signals only. We determined that the Lyapunov spectrum can be considered as the most expected method to evaluate chaotic behavior of scalp EEG recordings and to be robust within noises. Obtained results are compared to the independent component analysis (ICA) and largest Lyapunov exponent. The results of detecting epilepsy are compared to diagnosis from medical doctors in case of typical general epilepsy.
Lyapunov inequalities for Partial Differential Equations at radial higher eigenvalues
Canada, Antonio
2011-01-01
This paper is devoted to the study of $L_{p}$ Lyapunov-type inequalities ($ \\ 1 \\leq p \\leq +\\infty$) for linear partial differential equations at radial higher eigenvalues. More precisely, we treat the case of Neumann boundary conditions on balls in $\\real^{N}$. It is proved that the relation between the quantities $p$ and $N/2$ plays a crucial role to obtain nontrivial and optimal Lyapunov inequalities. By using appropriate minimizing sequences and a detailed analysis about the number and distribution of zeros of radial nontrivial solutions, we show significant qualitative differences according to the studied case is subcritical, supercritical or critical.
ANALYSIS OF MOTORCAR COURSE-KEEPING STABILITY
Directory of Open Access Journals (Sweden)
Makarov, V.
2012-06-01
Full Text Available The generalized scheme and graph-model with factors influencing the motorcar course-keeping stability are suggested. The analysis of possible variants improving the motorcar course-keeping stability is presented in the graph-model.
Using Lyapunov function to design optimal controller for AQM routers
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; YE Cheng-qing; MA Xue-ying; CHEN Yan-hua; LI Xin
2007-01-01
It was shown that active queue management schemes implemented in the routers of communication networks supporting transmission control protocol (TCP) flows can be modelled as a feedback control system. In this paper based on Lyapunov function we developed an optimal controller to improve active queue management (AQM) router's stability and response time,which are often in conflict with each other in system performance. Ns-2 simulations showed that optimal controller outperforms PI controller significantly.
Bohmian quantum mechanical and classical Lyapunov exponents for kicked rotor
Energy Technology Data Exchange (ETDEWEB)
Zheng Yindong [Department of Physics, University of North Texas, Denton, TX 76203-1427 (United States); Kobe, Donald H. [Department of Physics, University of North Texas, Denton, TX 76203-1427 (United States)], E-mail: kobe@unt.edu
2008-04-15
Using de Broglie-Bohm approach to quantum theory, we show that the kicked rotor at quantum resonance exhibits quantum chaos for the control parameter K above a threshold. Lyapunov exponents are calculated from the method of Benettin et al. for bounded systems for both the quantum and classical kicked rotor. In the chaotic regime we find stability regions for control parameters equal to even and odd multiples of {pi}, but the quantum regions are only remnants of the classical ones.
Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect
Kelly, Cónall
2016-09-01
We investigate the asymptotic behaviour of a reduced αΩ-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the α-effect results in a system with state-dependent stochastic perturbations. By computing the upper Lyapunov exponent of the linearised model, we can identify regions of instability and stability in probability for the equilibrium of the nonlinear model; in this case the equilibrium solution corresponds to a magnetic field that has undergone catastrophic quenching. These regions are compared to regions of exponential mean-square stability and regions of sub- and super-criticality in the unperturbed linearised model. Prior analysis in the literature which focuses on these latter regions does not adequately address the corresponding transition in the nonlinear stochastic model. Finally we provide a visual representation of the influence of drift non-normality and perturbation intensity on these regions.
Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed
2017-02-01
As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable.
Liu, Hongyang; Ou, Yan; Hu, Jun; Liu, Tingting
2010-04-01
This paper investigates the problem of stability analysis for bidirectional associative memory (BAM) neural networks with Markovian jumping parameters. Some new delay-dependent stochastic stability criteria are derived based on a novel Lyapunov-Krasovskii functional (LKF) approach. These new criteria based on the delay partitioning idea prove to be less conservative, since the conservatism could be notably reduced by thinning the delay partitioning. It is shown that the addressed stochastic BAM neural networks with Markovian jumping parameters are stochastically stable if three linear matrix inequalities (LMIs) are feasible. The feasibility of the LMIs can be readily checked by the Matlab LMI toolbox. A numerical example is provided to show the effectiveness and advantage of the proposed technique.
Institute of Scientific and Technical Information of China (English)
李安; 宋新宇; 王志祥
2011-01-01
该文研究了非线性微分方程关于初始时刻偏差的实用稳定性,利用扰动Lyapunov函数得到了几个非线性动力系统关于初始时刻偏差的实用稳定性准则,所得结论丰富了非线性微分方程关于初始时刻偏差的实用稳定性理论.%In this paper, the practical stability of nonlinear differential equations with solutions starting off with different initial times is investigated. Several practical stability criteria of nonlinear dynamical systems relative to initial time difference are presented by perturbing Lyapunov functions. The results enrich the theory on practical stability of nonlinear differential equations relative to initial time difference.
Lyapunov Function Synthesis - Algorithm and Software
DEFF Research Database (Denmark)
Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer
2016-01-01
In this paper we introduce an algorithm for the synthesis of polynomial Lyapunov functions for polynomial vector fields. The Lyapunov function is a continuous piecewisepolynomial defined on simplices, which compose a collection of simplices. The algorithm is elaborated and crucial features...
Rank-one LMIs and Lyapunov's inequality
Henrion, D.; Meinsma, Gjerrit
2001-01-01
We describe a new proof of the well-known Lyapunov's matrix inequality about the location of the eigenvalues of a matrix in some region of the complex plane. The proof makes use of standard facts from quadratic and semi-definite programming. Links are established between the Lyapunov matrix,
Rank-one LMIs and Lyapunov's inequality
Henrion, D.; Meinsma, G.
2001-01-01
We describe a new proof of the well-known Lyapunov's matrix inequality about the location of the eigenvalues of a matrix in some region of the complex plane. The proof makes use of standard facts from quadratic and semi-definite programming. Links are established between the Lyapunov matrix, rank-on
Lyapunov Function Synthesis - Algorithm and Software
DEFF Research Database (Denmark)
Leth, Tobias; Sloth, Christoffer; Wisniewski, Rafal
2016-01-01
In this paper we introduce an algorithm for the synthesis of polynomial Lyapunov functions for polynomial vector fields. The Lyapunov function is a continuous piecewisepolynomial defined on simplices, which compose a collection of simplices. The algorithm is elaborated and crucial features...
Yang, Hong-liu; Radons, Günter; Kantz, Holger
2012-12-14
The estimation of Lyapunov exponents from time series suffers from the appearance of spurious Lyapunov exponents due to the necessary embedding procedure. Separating true from spurious exponents poses a fundamental problem which is not yet solved satisfactorily. We show, in this Letter, analytically and numerically that covariant Lyapunov vectors associated with true exponents lie in the tangent space of the reconstructed attractor. Therefore, we use the angle between the covariant Lyapunov vectors and the tangent space of the reconstructed attractor to identify the true Lyapunov exponents. The usefulness of our method, also for noisy situations, is demonstrated by applications to data from model systems and a NMR laser experiment.
Stability Analysis of ISS Medications
Wotring, V. E.
2014-01-01
the United States Pharmacopeia (USP) to measure the amount of intact active ingredient, identify degradation products and measure their amounts. Some analyses were conducted by an independent analytical laboratory, but certain (Schedule) medications could not be shipped to their facility and were analyzed at JSC. RESULTS Nine medications were analyzed with respect to active pharmaceutical ingredient (API) and degradant amounts. Results were compared to the USP requirements for API and degradants/impurities content for every FDA-approved medication. One medication met USP requirements at 5 months after its expiration date. Four of the nine (44% of those tested) medications tested met USP requirements up to 8 months post-expiration. Another 3 medications (33% of those tested) met USP guidelines 2-3 months before expiration. One medication, a compound classed by the FDA as a dietary supplement and sometimes used as a sleep aid, failed to meet USP requirements at 11 months post-expiration. CONCLUSION Analysis of each medication at a single time point provides limited information on the stability of a medication stored in particular conditions; it is not possible to predict how long a medication may be safe and effective from these data. Notwithstanding, five of the nine medications tested (56%) met USP requirements for API and degradants/impurities at least 5 months past expiration dates. The single compound that failed to meet USP requirements is not regulated as strictly as prescription medications are during manufacture; it is unknown if this medication would have met the requirements prior to flight. Notably, it was the furthest beyond its expiration date. Only more comprehensive analysis of flight-aged samples compared to appropriate ground controls will permit determination of spaceflight effects on medication stability.
Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors
Elmetennani, Shahrazed
2016-11-09
This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature to track a set reference despite the unpredictable varying working conditions. In this brief, a bilinear model-based robust Lyapunov control is proposed to achieve the control objectives with robustness to the environmental changes. The bilinear model is a reduced order approximate representation of the solar collector, which is derived from the hyperbolic distributed equation describing the heat transport dynamics by means of a dynamical Gaussian interpolation. Using the bilinear approximate model, a robust control strategy is designed applying Lyapunov stability theory combined with a phenomenological representation of the system in order to stabilize the tracking error. On the basis of the error analysis, simulation results show good performance of the proposed controller, in terms of tracking accuracy and convergence time, with limited measurement even under unfavorable working conditions. Furthermore, the presented work is of interest for a large category of dynamical systems knowing that the solar collector is representative of physical systems involving transport phenomena constrained by unknown external disturbances.
Lyapunov exponent of chaos generated by acousto-optic modulators with feedback
Ghosh, Anjan K.; Verma, Pramode
2011-01-01
Generation of chaos from acousto-optic modulators with an electronic feedback has been studied for several years. Such chaotic signals have an important application in providing secure encryption in free-space optical communication systems. Lyapunov exponent is an important parameter for analysis of chaos generated by a nonlinear system. The Lyapunov exponent of an acousto-optic system is determined and calculated in this paper to understand the dependence of the chaotic response on the system parameters such as bias, feedback gain, input intensity and initial condition exciting the cell. Analysis of chaos using Lyapunov exponent is consistent with bifurcation analysis and is useful in encrypting data signals.
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, L; Pettini, M; Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-01-01
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.
Sign Stability via Root Locus Analysis
Gibson, Travis E
2015-01-01
With the rise of network science old topics in ecology and economics are resurfacing. One such topic is structural stability (often referred to as qualitative stability or sign stability). A system is deemed structurally stable if the system remains stable for all possible parameter variations so long as the parameters do not change sign. This type of stability analysis is appealing when studying real systems as the underlying stability result only requires the scientist or engineer to know the sign of the parameters in the model and not the specific values. The necessary and sufficient conditions for qualitative stability however are opaque. In order to shed light on those conditions root locus analysis is employed. This technique allows us to illustrate the necessary conditions for qualitative stability.
Energy Technology Data Exchange (ETDEWEB)
Kwon, O.M., E-mail: madwind@chungbuk.ac.k [School of Electrical Engineering, Chungbuk National University, Cheongju (Korea, Republic of); Lee, S.M., E-mail: moony@daegu.ac.k [School of Electronics Engineering, Daegu University, Kyongsan (Korea, Republic of); Park, Ju H., E-mail: jessie@ynu.ac.k [Department of Electrical Engineering, Yeungnam University, Kyongsan (Korea, Republic of)
2010-02-22
This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).
The Variation and Stability Analysis of Wheat Dough Stability Time
Institute of Scientific and Technical Information of China (English)
TIAN Ji-chun; HU Rui-bo; DENG Zhi-ying; WANG Yan-xun
2007-01-01
Farinograph dough stability time is an important index for classifying wheat, and it often indicates the most appropriate end use for the wheat cultivars. This study aimed at the problem of large fluctuations in dough stability time that occurs during the commercial wheat production. The variations in the dough stability time and its consistency across locations and years were analyzed using 12 principal high-quality wheat cultivars (varieties) obtained from Shandong Province,China, which were grown at nine different locations for three successive years. The results showed that the coefficient of variation for the dough stability time ranged from 24.29 to 49.60% across different varieties, locations, and years. Additive main effects and multiplicative interaction (AMMI) analysis indicated that there were significant interactions for the dough stability time between the varieties, the growth locations, and the years. The genotype effect was the most noticeable, followed by the interaction of the genotype and the environment. The environmental effect was the least significant. The interactions between the varieties and the locations differ considerably, however, each cultivar (variety) apparently has a specific adaptability to the growth location. Therefore, for the successful commercial scale production of the high-quality wheat varieties, both the selection of proper cultivars and its most suitable growth locations to meet the desired requirements for the dough mixing stability time are important.
Institute of Scientific and Technical Information of China (English)
Su Weiwei; Chen Yiming
2008-01-01
Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.
Lyapunov vectors and assimilation in the unstable subspace: theory and applications
Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna
2013-06-01
Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.
Short-Term Forecasting of Urban Water Consumption Based on the Largest Lyapunov Exponent
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were examined by means of the largest Lyapunov exponent and correlation dimension. By using the largest Lyapunov exponent a short-term forecasting model for urban water consumption was developed, which was compared with the artificial neural network (ANN) approach in a case study. The result indicates that the model based on the largest Lyapunov exponent has higher prediction precision and forecasting stability than the ANN method, and its forecasting mean relative error is 9.6% within its maximum predictable time scale while it is 60.6% beyond the scale.
Application of local Lyapunov exponents to maneuver design and navigation in the three-body problem
Anderson, Rodney L.; Lo, Martin W.; Born, George H.
2003-01-01
Dynamical systems theory has recently been employed to design trajectories within the three-body problem for several missions. This research has applied one stability technique, the calculation of local Lyapunov exponents, to such trajectories. Local Lyapunov exponents give an indication of the effects that perturbations or maneuvers will have on trajectories over a specified time. A numerical comparison of local Lyapunov exponents was first made with the distance random perturbations traveled from a nominal trajectory, and the local Lyapunov exponents were found to correspond well with the perturbations that caused the greatest deviation from the nominal. This would allow them to be used as an indicator of the points where it would be important to reduce navigation uncertainties.
Application of local Lyapunov exponents to maneuver design and navigation in the three-body problem
Anderson, Rodney L.; Lo, Martin W.; Born, George H.
2003-01-01
Dynamical systems theory has recently been employed to design trajectories within the three-body problem for several missions. This research has applied one stability technique, the calculation of local Lyapunov exponents, to such trajectories. Local Lyapunov exponents give an indication of the effects that perturbations or maneuvers will have on trajectories over a specified time. A numerical comparison of local Lyapunov exponents was first made with the distance random perturbations traveled from a nominal trajectory, and the local Lyapunov exponents were found to correspond well with the perturbations that caused the greatest deviation from the nominal. This would allow them to be used as an indicator of the points where it would be important to reduce navigation uncertainties.
Muralisankar, S; Manivannan, A; Balasubramaniam, P
2015-09-01
The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov-Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.
Lyapunov instabilities of Lennard-Jones fluids.
Yang, Hong-liu; Radons, Günter
2005-03-01
Recent work on many-particle systems reveals the existence of regular collective perturbations corresponding to the smallest positive Lyapunov exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these modes have been found only for hard-core systems. Here we report results on Lyapunov spectra and Lyapunov vectors (LVs) for Lennard-Jones fluids. By considering the Fourier transform of the coordinate fluctuation density u((alpha)) (x,t) , it is found that the LVs with lambda approximately equal to 0 are highly dominated by a few components with low wave numbers. These numerical results provide strong evidence that hydrodynamic Lyapunov modes do exist in soft-potential systems, although the collective Lyapunov modes are more vague than in hard-core systems. In studying the density and temperature dependence of these modes, it is found that, when the value of the Lyapunov exponent lambda((alpha)) is plotted as function of the dominant wave number k(max) of the corresponding LV, all data from simulations with different densities and temperatures collapse onto a single curve. This shows that the dispersion relation lambda((alpha)) vs k(max) for hydrodynamical Lyapunov modes appears to be universal for the low-density cases studied here. Despite the wavelike character of the LVs, no steplike structure exists in the Lyapunov spectrum of the systems studied here, in contrast to the hard-core case. Further numerical simulations show that the finite-time LEs fluctuate strongly. We have also investigated localization features of LVs and propose a length scale to characterize the Hamiltonian spatiotemporal chaotic states.
Farivar, Faezeh; Shoorehdeli, Mahdi Aliyari
2012-01-01
In this paper, fault tolerant synchronization of chaotic gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control is investigated. Taking the general nature of faults in the slave system into account, a new synchronization scheme, namely, fault tolerant synchronization, is proposed, by which the synchronization can be achieved no matter whether the faults and disturbances occur or not. By making use of a slave observer and a Lyapunov rule-based fuzzy control, fault tolerant synchronization can be achieved. Two techniques are considered as control methods: classic Lyapunov-based control and Lyapunov rule-based fuzzy control. On the basis of Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are obtained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. Two proposed methods are compared. The Lyapunov rule-based fuzzy control can compensate for the actuator faults and disturbances occurring in the slave system. Numerical simulation results demonstrate the validity and feasibility of the proposed method for fault tolerant synchronization.
Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System
Directory of Open Access Journals (Sweden)
Zixin Liu
2013-01-01
Full Text Available This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation. The proposed method employs an improved Wirtinger-type inequality for constructing a new Lyapunov functional with triple integral items. By using the convex expression of the nonlinear perturbation function, the original nonlinear Lur'e system is transformed into a linear uncertain system. Based on the Lyapunov stable theory, some novel delay-depended stability criteria for the researched system are established in terms of linear matrix inequality technique. Three numerical examples are presented to illustrate the validity of the main results.
Stability Analysis of Path-vector Routing
Dimitri, Papadimitriou
2012-01-01
Most studies on path-vector routing stability have been conducted empirically by means of ad-hoc analysis of BGP data traces. None of them consider prior specification of an analytic method including the use of stability measurement metrics for the systematic analysis of BGP traces and associated meta-processing for determining the local state of the routing system. In this paper, we define a set of metrics that characterize the local stability properties of path-vector routing such as BGP (Border Gateway Protocol). By means of these stability metrics, we propose a method to analyze the effects of BGP policy- and protocol-induced instability on local routers.
Analysis of Path-vector Routing Stability
Dimitri, Papadimitriou
2012-01-01
Most studies on path-vector routing stability have been conducted empirically by means of ad-hoc analysis of BGP data traces. None of them consider prior specification of an analytic method including the use of stability measurement metrics for the systematic analysis of BGP traces and associated meta-processing for determining the local state of the routing system. In this paper, we define a set of metrics that characterize the local stability properties of path-vector routing such as BGP (Border Gateway Protocol). By means of these stability metrics, we propose a method to analyze the effects of BGP policy- and protocol-induced instability on local routers.
Stability analysis of a simple rheonomic nonholonomic constrained system
Liu, Chang; Liu, Shi-Xing; Mei, Feng-Xing
2016-12-01
It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems. Project supported by the National Natural Science Foundation of China (Grant Nos. 11272050, 11202090, 11472124, 11572034, and 11572145), the Science and Technology Research Project of Liaoning Province, China (Grant No. L2013005), China Postdoctoral Science Foundation (Grant No. 2014M560203), and the Doctor Start-up Fund in Liaoning Province of China (Grant No. 20141050).
Stability of the Stochastic Differential Equations
Klimešová, M.
2015-01-01
Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provide some very powerful instruments in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems. The study of exponential stability of the moments makes natural the conside...
Pseudo-Lyapunov exponents and predictability of Hodgkin-Huxley neuronal network dynamics.
Sun, Yi; Zhou, Douglas; Rangan, Aaditya V; Cai, David
2010-04-01
We present a numerical analysis of the dynamics of all-to-all coupled Hodgkin-Huxley (HH) neuronal networks with Poisson spike inputs. It is important to point out that, since the dynamical vector of the system contains discontinuous variables, we propose a so-called pseudo-Lyapunov exponent adapted from the classical definition using only continuous dynamical variables, and apply it in our numerical investigation. The numerical results of the largest Lyapunov exponent using this new definition are consistent with the dynamical regimes of the network. Three typical dynamical regimes-asynchronous, chaotic and synchronous, are found as the synaptic coupling strength increases from weak to strong. We use the pseudo-Lyapunov exponent and the power spectrum analysis of voltage traces to characterize the types of the network behavior. In the nonchaotic (asynchronous or synchronous) dynamical regimes, i.e., the weak or strong coupling limits, the pseudo-Lyapunov exponent is negative and there is a good numerical convergence of the solution in the trajectory-wise sense by using our numerical methods. Consequently, in these regimes the evolution of neuronal networks is reliable. For the chaotic dynamical regime with an intermediate strong coupling, the pseudo-Lyapunov exponent is positive, and there is no numerical convergence of the solution and only statistical quantifications of the numerical results are reliable. Finally, we present numerical evidence that the value of pseudo-Lyapunov exponent coincides with that of the standard Lyapunov exponent for systems we have been able to examine.
Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
Kuznetsov, N. V.; Alexeeva, T. A.; Leonov, G. A.
2014-01-01
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singula...
Covariant Lyapunov vectors for rigid disk systems.
Bosetti, Hadrien; Posch, Harald A
2010-10-05
We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.
Infinitesimal Lyapunov functions and singular-hyperbolicity
Araujo, Vitor
2012-01-01
We present an extension of the notion of infinitesimal Lyapunov function to singular flows on three-dimensional manifolds, and show how this technique provides a characterization of partially hyperbolic structures for invariant sets for such flows, and also of singular-hyperbolicity. In the absence of singularities, we can also rephrase uniform hyperbolicity with the language of infinitesimal Lyapunov functions. These conditions are expressed using the vector field X and its space derivative DX together with an infinitesimal Lyapunov function only and are reduced to checking that a certain symmetric operator is positive definite on the trapping region: we show how to express partial hyperbolicity using only the interplay between the infinitesimal generator X of the flow X_t, its derivative DX and the infinitesimal Lyapunov function.
Profile Orientation and Slope Stability Analysis
Directory of Open Access Journals (Sweden)
Zhe-Ping Shen
2016-01-01
Full Text Available This paper presents an analysis of soil slope stability using a terrestrial laser scanner, particle swarm optimization, and the force equilibrium method. The aim of this study was to demonstrate that a slope needed to be analyzed in many different directions in order to assess its stability conclusively, rather than using just one cross-sectional profile to represent the entire slope. To achieve this purpose, this study illustrates how a particle swarm optimization algorithm can be successfully incorporated into the analysis with slope stability analysis software, STABL. This study compares results obtained with those of previous studies and makes important observations.
The computer in shell stability analysis
Almroth, B. O.; Starnes, J. H., Jr.
1975-01-01
Some examples in which the high-speed computer has been used to improve the static stability analysis capability for general shells are examined. The fundamental concepts of static stability are reviewed with emphasis on the differences between linear bifurcation buckling and nonlinear collapse. The analysis is limited to the stability of conservative systems. Three examples are considered. The problem of cylinders subjected to bending loads is used as an example to illustrate that a simple structure can have a sufficiently complicated nonlinear behavior to require a computer analysis for accurate results. An analysis of the problems involved in the modeling of stiffening elements in plate and shell structures illustrates the necessity that the analyst recognizes all important deformation modes. The stability analysis of the Skylab structure indicates the size of problems that can be solved with current state-of-the-art capability.
Power system stability modelling, analysis and control
Sallam, Abdelhay A
2015-01-01
This book provides a comprehensive treatment of the subject from both a physical and mathematical perspective and covers a range of topics including modelling, computation of load flow in the transmission grid, stability analysis under both steady-state and disturbed conditions, and appropriate controls to enhance stability.
Robust stability analysis of a class of neural networks with discrete time delays.
Faydasicok, Ozlem; Arik, Sabri
2012-05-01
This paper studies the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete constant time delays under parameter uncertainties. The class of the neural network considered in this paper employs the activation functions which are assumed to be continuous and slope-bounded but not required to be bounded or differentiable. We conduct a stability analysis by exploiting the stability theory of Lyapunov functionals and the theory of Homomorphic mapping to derive some easily verifiable sufficient conditions for existence, uniqueness and global asymptotic stability of the equilibrium point. The conditions obtained mainly establish some time-independent relationships between the network parameters of the neural network. We make a detailed comparison between our results and the previously published corresponding results. This comparison proves that our results are new and improve and generalize the results derived in the past literature. We also give some illustrative numerical examples to show the effectiveness and applicability of our proposed stability results.
Jacobi stability analysis of Rikitake system
Gupta, M. K.; Yadav, C. K.
2016-06-01
We study the Rikitake system through the method of differential geometry, i.e. Kosambi-Cartan-Chern (KCC) theory for Jacobi stability analysis. For applying KCC theory we reformulate the Rikitake system as two second-order nonlinear differential equations. The five KCC invariants are obtained which express the intrinsic properties of nonlinear dynamical system. The deviation curvature tensor and its eigenvalues are obtained which determine the stability of the system. Jacobi stability of the equilibrium points is studied and obtain the conditions for stability. We study the dynamics of Rikitake system which shows the chaotic behaviour near the equilibrium points.
Computer Aided Transient Stability Analysis
Directory of Open Access Journals (Sweden)
Nihad M. Al-Rawi
2007-01-01
Full Text Available A program for handling and improving the transient stability of the Iraqi Super Grid electrical network was developed. The idea was demonstrated by applying it to the outages of the main generating units. The methodology was built upon a state of increasing power transfer through the healthy portion of network during disturbances. There were three parts concerned; the first part was the developing of the load flow program using fast decoupled method and the transient stability program using Modified Eulers method in the step by step solution, the second part was the engagement between the two programs, the third part was the application of the new program on the Iraqi supper grid network (400 kV.
Stability Analysis of State Saturation 2D Discrete Time-Delay Systems Based on F-M Model
Directory of Open Access Journals (Sweden)
Dongyan Chen
2013-01-01
Full Text Available The problem of stability analysis is investigated for a class of state saturation two-dimensional (2D discrete time-delay systems described by the Fornasini-Marchesini (F-M model. The delay is allowed to be a bounded time-varying function. By constructing the delay-dependent 2D discrete Lyapunov functional and introducing a nonnegative scalar β, a sufficient condition is proposed to guarantee the global asymptotic stability of the addressed systems. Subsequently, the criterion is converted into the linear matrix inequalities (LMIs which can be easily tested by using the standard numerical software. Finally, two numerical examples are given to show the effectiveness of the proposed stability criterion.
A Dynamic Analysis for an Anaerobic Digester: Stability and Bifurcation Branches
Directory of Open Access Journals (Sweden)
Alejandro Rincón
2014-01-01
Full Text Available This work presents a dynamic analysis for an anaerobic digester, supported on the analytical application of the indirect Lyapunov method. The mass-balance model considered is based on two biological reaction pathways and involves both Monod and Haldane representations of the specific biomass growth rates. The dilution rate, the influent concentration of chemical oxygen demand (COD, and the influent concentration of volatile fatty acids (VFA are considered as stability parameters. Several characteristics are determined analytically for the normal operation equilibrium point: (i equilibrium coordinates, (ii parameter conditions that lead to positive values of the equilibrium state variables, (iii parameter conditions for locally stable nature of the equilibrium, (iv coordinates for the local bifurcation points—fold and transcritical—, and (v coordinates of the crossing between bifurcation points. These factors are computed analytically and explicitly as expressions of the dilution rate and the influent concentrations of COD and VFA.
Singh, H P; Sukavanam, N
2012-01-01
This paper proposes a new adaptive neural network based control scheme for switched linear systems with parametric uncertainty and external disturbance. A key feature of this scheme is that the prior information of the possible upper bound of the uncertainty is not required. A feedforward neural network is employed to learn this upper bound. The adaptive learning algorithm is derived from Lyapunov stability analysis so that the system response under arbitrary switching laws is guaranteed uniformly ultimately bounded. A comparative simulation study with robust controller given in [Zhang L, Lu Y, Chen Y, Mastorakis NE. Robust uniformly ultimate boundedness control for uncertain switched linear systems. Computers and Mathematics with Applications 2008; 56: 1709-14] is presented.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers
Bokelmann, Kevin; Russell, Ryan P.; Lantoine, Gregory
2013-01-01
Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.
Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers
Bokelmann, Kevin; Russell, Ryan P.; Lantoine, Gregory
2013-01-01
Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.
Design of Connectivity Preserving Flocking Using Control Lyapunov Function
Directory of Open Access Journals (Sweden)
Bayu Erfianto
2016-01-01
Full Text Available This paper investigates cooperative flocking control design with connectivity preserving mechanism. During flocking, interagent distance is measured to determine communication topology of the flocks. Then, cooperative flocking motion is built based on cooperative artificial potential field with connectivity preserving mechanism to achieve the common flocking objective. The flocking control input is then obtained by deriving cooperative artificial potential field using control Lyapunov function. As a result, we prove that our flocking protocol establishes group stabilization and the communication topology of multiagent flocking is always connected.
Zhao, Xueyan; Deng, Feiqi
2016-07-01
In this paper, a particular property of Lyapunov functions for functional differential equations (FDEs) is developed, that is the direct dependence of the signs of the derivatives of the Lyapunov functions on the initial data. This property implies that the derivatives of the Lyapunov functions for FDEs cannot be guaranteed to be negative definite generally, and then makes the FDEs differ from the ordinary differential equations constitutionally. With this property, we give some enlightenments for the research methods for establishing stability theorems or criteria for FDEs, which may help us to form a common view about the choice of the investigation methods on the stability of FDEs. The conclusion is stated in both the deterministic and stochastic versions. Two illustrative examples are given to show and verify our conclusion through the paper.
DEFF Research Database (Denmark)
Ribard, Nicolas; Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
In the paper, we strive to develop an algorithm that simultaneously computes a polynomial control and a polynomial Lyapunov function. This ensures asymptotic stability of the designed feedback system. The above problem is translated to a certificate of positivity. To this end, we use the represen......In the paper, we strive to develop an algorithm that simultaneously computes a polynomial control and a polynomial Lyapunov function. This ensures asymptotic stability of the designed feedback system. The above problem is translated to a certificate of positivity. To this end, we use...... the representation of the given control system in Bernstein basis. Subsequently, the control synthesis problem is reduced to finite number of evaluations of a polynomial on vertices of cubes in the space of parameters representing admissible controls and Lyapunov functions....
Are Bred Vectors The Same As Lyapunov Vectors?
Kalnay, E.; Corazza, M.; Cai, M.
Regional loss of predictability is an indication of the instability of the underlying flow, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. The stability properties of evolving flows have been studied using Lyapunov vectors (e.g., Alligood et al, 1996, Ott, 1993, Kalnay, 2002), singular vectors (e.g., Lorenz, 1965, Farrell, 1988, Molteni and Palmer, 1993), and, more recently, with bred vectors (e.g., Szunyogh et al, 1997, Cai et al, 2001). Bred vectors (BVs) are, by construction, closely related to Lyapunov vectors (LVs). In fact, after an infinitely long breeding time, and with the use of infinitesimal ampli- tudes, bred vectors are identical to leading Lyapunov vectors. In practical applications, however, bred vectors are different from Lyapunov vectors in two important ways: a) bred vectors are never globally orthogonalized and are intrinsically local in space and time, and b) they are finite-amplitude, finite-time vectors. These two differences are very significant in a dynamical system whose size is very large. For example, the at- mosphere is large enough to have "room" for several synoptic scale instabilities (e.g., storms) to develop independently in different regions (say, North America and Aus- tralia), and it is complex enough to have several different possible types of instabilities (such as barotropic, baroclinic, convective, and even Brownian motion). Bred vectors share some of their properties with leading LVs (Corazza et al, 2001a, 2001b, Toth and Kalnay, 1993, 1997, Cai et al, 2001). For example, 1) Bred vectors are independent of the norm used to define the size of the perturba- tion. Corazza et al. (2001) showed that bred vectors obtained using a potential enstro- phy norm were indistinguishable from bred vectors obtained using a streamfunction squared norm, in contrast with singular vectors. 2) Bred vectors are independent of the length of the rescaling period as long as the
Research on the stability of control systems described by fractional-order transfer functions
Institute of Scientific and Technical Information of China (English)
Zeng Qingshan; Zhu Xinjian; Cao Guangyi
2005-01-01
The stability of control systems described by fractional-order transfer function form is mainly investigated. The stability analysis of integer-order linear systems was extended to the fractional-order control systems. The stability definition of fractional-order linear control systems is presented in terms of the Lyapunov's stability theory. Using the theorems of the Mittag-Leffler function in two parameters directly derives the stability conclusion. The illustrative examples are also given by simulation results.
Stability analysis of free piston Stirling engines
Bégot, Sylvie; Layes, Guillaume; Lanzetta, François; Nika, Philippe
2013-03-01
This paper presents a stability analysis of a free piston Stirling engine. The model and the detailed calculation of pressures losses are exposed. Stability of the machine is studied by the observation of the eigenvalues of the model matrix. Model validation based on the comparison with NASA experimental results is described. The influence of operational and construction parameters on performance and stability issues is exposed. The results show that most parameters that are beneficial for machine power seem to induce irregular mechanical characteristics with load, suggesting that self-sustained oscillations could be difficult to maintain and control.
On the bound of the Lyapunov exponents for the fractional differential systems.
Li, Changpin; Gong, Ziqing; Qian, Deliang; Chen, YangQuan
2010-03-01
In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, and complex networks. Although an autonomous system cannot define a dynamical system in the sense of semigroup because of the memory property determined by the fractional derivative, we can still use the Lyapunov exponents to discuss its dynamical evolution. In this paper, we first define the Lyapunov exponents for fractional differential systems then estimate the bound of the corresponding Lyapunov exponents. For linear fractional differential system, the bounds of its Lyapunov exponents are conveniently derived which can be regarded as an example for the theoretical results established in this paper. Numerical example is also included which supports the theoretical analysis.
Wen, Guanghui; Yu, Wenwu; Hu, Guoqiang; Cao, Jinde; Yu, Xinghuo
2015-12-01
This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results.
A survey of quantum Lyapunov control methods.
Cong, Shuang; Meng, Fangfang
2013-01-01
The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed.
Lyapunov exponents computation for hybrid neurons.
Bizzarri, Federico; Brambilla, Angelo; Gajani, Giancarlo Storti
2013-10-01
Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational model. Hybrid neurons do not belong to this wide class of systems since they are intrinsically non-smooth owing to the impact and sometimes switching model used to describe the integrate-and-fire (I&F) mechanism. In this paper we show how a variational model can be defined also for this class of neurons by resorting to saltation matrices. This extension allows the computation of Lyapunov exponent spectrum of hybrid neurons and of networks made up of them through a standard numerical approach even in the case of neurons firing synchronously.
Stabilizing Randomly Switched Systems
Chatterjee, Debasish
2008-01-01
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control design
Linear stability analysis of heated parallel channels
Nourbakhsh, H. P.; Isbin, H. S.
An analyis is presented of thermal hydraulic stability of flow in parallel channels covering the range from inlet subcooling to exit superheat. The model is based on a one-dimensional drift velocity formulation of the two phase flow conservation equations. The system of equations is linearized by assuming small disturbances about the steady state. The dynamic response of the system to an inlet flow perturbation is derived yielding the characteristic equation which predicts the onset of instabilities. A specific application is carried out for homogeneous and regional uniformly heated systems. The particular case of equal characteristic frequencies of two-phase and single phase vapor region is studied in detail. The D-partition method and the Mikhailov stability criterion are used for determining the marginal stability boundary. Stability predictions from the present analysis are compared with the experimental data from the solar test facility.
Stability analysis of a system coupled to a transport equation using integral inequalities
Baudouin, Lucie; Seuret, Alexandre; Safi, Mohammed
2016-01-01
International audience; We address the stability of a system of ordinary differential equations coupled with a transport partial differential equation, using a Lyapunov functional approach. This system can also be interpreted as a finite dimensional system subject to a state delay. Inspired from recent developments on time-delay systems, a novel method to assess stability of such a class of coupled systems is developed here. We will specifically take advantage of a polynomial approximation of...
The Lyapunov dimension and its estimation via the Leonov method
Energy Technology Data Exchange (ETDEWEB)
Kuznetsov, N.V., E-mail: nkuznetsov239@gmail.com
2016-06-03
Highlights: • Survey on effective analytical approach for Lyapunov dimension estimation, proposed by Leonov, is presented. • Invariance of Lyapunov dimension under diffeomorphisms and its connection with Leonov method are demonstrated. • For discrete-time dynamical systems an analog of Leonov method is suggested. - Abstract: Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, proposed by G.A. Leonov in 1991. The Leonov method is based on the direct Lyapunov method with special Lyapunov-like functions. The advantage of the method is that it allows one to estimate the Lyapunov dimension of invariant sets without localization of the set in the phase space and, in many cases, to get effectively an exact Lyapunov dimension formula. In this work the invariance of the Lyapunov dimension with respect to diffeomorphisms and its connection with the Leonov method are discussed. For discrete-time dynamical systems an analog of Leonov method is suggested. In a simple but rigorous way, here it is presented the connection between the Leonov method and the key related works: Kaplan and Yorke (the concept of the Lyapunov dimension, 1979), Douady and Oesterlé (upper bounds of the Hausdorff dimension via the Lyapunov dimension of maps, 1980), Constantin, Eden, Foiaş, and Temam (upper bounds of the Hausdorff dimension via the Lyapunov exponents and Lyapunov dimension of dynamical systems, 1985–90), and the numerical calculation of the Lyapunov exponents and dimension.
A statistical approach to estimate the LYAPUNOV spectrum in disc brake squeal
Oberst, S.; Lai, J. C. S.
2015-01-01
The estimation of squeal propensity of a brake system from the prediction of unstable vibration modes using the linear complex eigenvalue analysis (CEA) in the frequency domain has its fair share of successes and failures. While the CEA is almost standard practice for the automotive industry, time domain methods and the estimation of LYAPUNOV spectra have not received much attention in brake squeal analyses. One reason is the challenge in estimating the true LYAPUNOV exponents and their discrimination against spurious ones in experimental data. A novel method based on the application of the ECKMANN-RUELLE matrices is proposed here to estimate LYAPUNOV exponents by using noise in a statistical procedure. It is validated with respect to parameter variations and dimension estimates. By counting the number of non-overlapping confidence intervals for LYAPUNOV exponent distributions obtained by moving a window of increasing size over bootstrapped same-length estimates of an observation function, a dispersion measure's width is calculated and fed into a BAYESIAN beta-binomial model. Results obtained using this method for benchmark models of white and pink noise as well as the classical HENON map indicate that true LYAPUNOV exponents can be isolated from spurious ones with high confidence. The method is then applied to accelerometer and microphone data obtained from brake squeal tests. Estimated LYAPUNOV exponents indicate that the pad's out-of-plane vibration behaves quasi-periodically on the brink to chaos while the microphone's squeal signal remains periodic.
Stabilisation of a class of 2-DOF underactuated mechanical systems via direct Lyapunov approach
Turker, Turker; Gorgun, Haluk; Cansever, Galip
2013-06-01
This paper represents an alternative stabilisation procedure for a class of two degree-of-freedom underactuated mechanical systems based on a set of transformations and a Lyapunov function. After simplifying dynamic equations of the system via partial feedback linearisation and coordinate changes, the stability of the system is provided with Lyapunov's direct method. Proposed control scheme is used on two different examples and asymptotic convergence for each system is proven by means of La Salle's invariance principle. The designed controller is successfully illustrated through numerical simulations for each example.
Stock market stability: Diffusion entropy analysis
Li, Shouwei; Zhuang, Yangyang; He, Jianmin
2016-05-01
In this article, we propose a method to analyze the stock market stability based on diffusion entropy, and conduct an empirical analysis of Dow Jones Industrial Average. Empirical results show that this method can reflect the volatility and extreme cases of the stock market.
Inertia theorems for operator Lyapunov inequalities
Sasane, AJ; Curtain, RF
2001-01-01
We study operator Lyapunov inequalities and equations for which the infinitesimal generator is not necessarily stable, but it satisfies the spectrum decomposition assumption and it has at most finitely many unstable eigenvalues. Moreover, the input or output operators are not necessarily bounded, bu
Lyapunov Function Synthesis - Infeasibility and Farkas' Lemma
DEFF Research Database (Denmark)
Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer
2017-01-01
In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector elds dened on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove...
Inertia theorems for operator Lyapunov inequalities
Sasane, AJ; Curtain, RF
2001-01-01
We study operator Lyapunov inequalities and equations for which the infinitesimal generator is not necessarily stable, but it satisfies the spectrum decomposition assumption and it has at most finitely many unstable eigenvalues. Moreover, the input or output operators are not necessarily bounded,
Controllability of semilinear matrix Lyapunov systems
Directory of Open Access Journals (Sweden)
Bhaskar Dubey
2013-02-01
Full Text Available In this article, we establish some sufficient conditions for the complete controllability of semilinear matrix Lyapunov systems involving Lipschitzian and non-Lipschitzian nonlinearities. In case of non-Lipschitzian nonlinearities, we assume that nonlinearities are of monotone type.
Lyapunov exponents for continuous random transformations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, the concept of Lyapunov exponent is generalized to random transformations that are not necessarily differentiable. For a class of random repellers and of random hyperbolic sets obtained via small perturbations of deterministic ones respectively, the new exponents are shown to coincide with the classical ones.
Stability Analysis for Switching of Discrete Linear Singular Systems%奇异离散线性系统的开关切换控制
Institute of Scientific and Technical Information of China (English)
郭晓丽; 李蔚; 慕小武
2006-01-01
In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.
GA and Lyapunov theory-based hybrid adaptive fuzzy controller for non-linear systems
Roy, Ananya; Das Sharma, Kaushik
2015-02-01
In this present article, a new hybrid methodology for designing stable adaptive fuzzy logic controllers (AFLCs) for a class of non-linear system is proposed. The proposed design strategy exploits the features of genetic algorithm (GA)-based stochastic evolutionary global search technique and Lyapunov theory-based local adaptation scheme. The objective is to develop a methodology for designing AFLCs with optimised free parameters and guaranteed closed-loop stability. Simultaneously, the proposed method introduces automation in the design process. The stand-alone Lyapunov theory-based design, GA-based design and proposed hybrid GA-Lyapunov design methodologies are implemented for two benchmark non-linear plants in simulation case studies with different reference signals and one experimental case study. The results demonstrate that the hybrid design methodology outperforms the other control strategies on the whole.
Lyapunov-based boundary feedback control in multi-reach canals
Institute of Scientific and Technical Information of China (English)
CEN LiHui; XI YuGeng
2009-01-01
This paper presents a Lyapunov-based approach to design the boundary feedback control for an open-channel network composed of a cascade of multi-reach canals, each described by a pair of Saint-Venant equations. The weighted sum of entropies of the multi-reaches is adopted to construct the Lyapunov function. The time derivative of the Lyapunov function is expressed by the water depth variations at the gate boundaries, based on which a class of boundary feedback controllers is presented to guarantee the local asymptotic closed-loop stability. The advantage of this approach is that only the water level depths at the gate boundaries are measured as the feedback.
The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance
Directory of Open Access Journals (Sweden)
Kun Liu
2015-01-01
Full Text Available The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body’s standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.
The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance.
Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang
2015-01-01
The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body's standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.
Zhang, Xian-Ming; Han, Qing-Long
2014-06-01
This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.
Stability analysis and design of fuzzy control system with bounded uncertain delays
Institute of Scientific and Technical Information of China (English)
Jianguo GUO; Juntao LI; Fengqi ZHOU; Jun ZHOU
2005-01-01
Fuzzy control problems for systems with bounded uncertain delays were studied.Based on Lyapunov stability theory and matrix theory,a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities (LMI) approach,and the global exponential stability of the closed-loop system was strictly proved.For a fuzzy control system with bounded uncertain delays,under the global exponential stability condition which is reduced to p linear matrix inequalities,the controller guarantees stability performances of state variables.Finally,the simulation shows the validity of the method in this paper.
Stability analysis of switched stochastic neural networks with time-varying delays.
Wu, Xiaotai; Tang, Yang; Zhang, Wenbing
2014-03-01
This paper is concerned with the global exponential stability of switched stochastic neural networks with time-varying delays. Firstly, the stability of switched stochastic delayed neural networks with stable subsystems is investigated by utilizing the mathematical induction method, the piecewise Lyapunov function and the average dwell time approach. Secondly, by utilizing the extended comparison principle from impulsive systems, the stability of stochastic switched delayed neural networks with both stable and unstable subsystems is analyzed and several easy to verify conditions are derived to ensure the exponential mean square stability of switched delayed neural networks with stochastic disturbances. The effectiveness of the proposed results is illustrated by two simulation examples.
Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method
Institute of Scientific and Technical Information of China (English)
Chen Yimei; Han Zhengzhi; Tang Houjun
2006-01-01
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.
Liu, Chuang; Lam, Hak-Keung; Fernando, Tyrone; Iu, Herbert Ho-Ching
2016-05-02
In this paper, we investigate the stability of Takagi-Sugeno fuzzy-model-based (FMB) functional observer-control system. When system states are not measurable for state-feedback control, a fuzzy functional observer is designed to directly estimate the control input instead of the system states. Although the fuzzy functional observer can reduce the order of the observer, it leads to a number of observer gains to be determined. Therefore, a new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. The proposed form is also in favor of applying separation principle to separately design the fuzzy controller and the fuzzy functional observer. To design the fuzzy controller with the consideration of system stability, higher order derivatives of Lyapunov function (HODLF) are employed to reduce the conservativeness of stability conditions. The HODLF generalizes the commonly used first-order derivative. By exploiting the properties of membership functions and the dynamics of the FMB control system, convex and relaxed stability conditions can be derived. Simulation examples are provided to show the relaxation of the proposed stability conditions and the feasibility of designed fuzzy functional observer-controller.
Institute of Scientific and Technical Information of China (English)
Wenjuan ZHANG; Li CHEN; Ning QU; Hai'an LIANG
2006-01-01
Landslide is one kind of geologic hazards that often happens all over the world. It brings huge losses to human life and property; therefore, it is very important to research it. This study focused in combination between single and regional landslide, traditional slope stability analysis method and reliability analysis method. Meanwhile, methods of prediction of slopes and reliability analysis were discussed.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Clustering and synchronization with positive Lyapunov exponents
Mendes, R V
1998-01-01
Clustering and correlation effects are frequently observed in chaotic systems in situations where, because of the positivity of the Lyapunov exponents, no dimension reduction is to be expected. In this paper, using a globally coupled network of Bernoulli units, one finds a general mechanism by which strong correlations and slow structures are obtained at the synchronization edge. A structure index is defined, which diverges at the transition points. Some conclusions are drawn concerning the construction of an ergodic theory of self-organization.
Linear Stability Analysis of Dynamical Quadratic Gravity
Ayzenberg, Dimitry; Yunes, Nicolas
2013-01-01
We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Control of acrobot based on Lyapunov function
Institute of Scientific and Technical Information of China (English)
赖旭芝; 吴敏; 佘锦华
2004-01-01
Fuzzy control based on Lyapunov function was employed to control the posture and the energy of an acrobot to make the transition from upswing control to balance control smoothly and stably. First, a control law based on Lyapunov function was used to control the angle and the angular velocity of the second link towards zero when the energy of the acrobot reaches the potential energy at the unstable straight-up equilibrium position in the upswing process. The controller based on Lyapunov function makes the second link straighten nature relatively to the first link. At the same time, a fuzzy controller was designed to regulate the parameters of the upper control law to keep the change of the energy of the acrobot to a minimum, so that the switching from upswing to balance can be properly carried out and the acrobot can enter the balance quickly. The results of simulation show that the switching from upswing to balance can be completed smoothly, and the control effect of the acrobot is improved greatly.
Reliability Analysis of High Rockfill Dam Stability
Directory of Open Access Journals (Sweden)
Ping Yi
2015-01-01
Full Text Available A program 3DSTAB combining slope stability analysis and reliability analysis is developed and validated. In this program, the limit equilibrium method is utilized to calculate safety factors of critical slip surfaces. The first-order reliability method is used to compute reliability indexes corresponding to critical probabilistic surfaces. When derivatives of the performance function are calculated by finite difference method, the previous iteration’s critical slip surface is saved and used. This sequential approximation strategy notably improves efficiency. Using this program, the stability reliability analyses of concrete faced rockfill dams and earth core rockfill dams with different heights and different slope ratios are performed. The results show that both safety factors and reliability indexes decrease as the dam’s slope increases at a constant height and as the dam’s height increases at a constant slope. They decrease dramatically as the dam height increases from 100 m to 200 m while they decrease slowly once the dam height exceeds 250 m, which deserves attention. Additionally, both safety factors and reliability indexes of the upstream slope of earth core rockfill dams are higher than that of the downstream slope. Thus, the downstream slope stability is the key failure mode for earth core rockfill dams.
New delay-dependent stability criteria for neural networks with time-varying interval delay
Energy Technology Data Exchange (ETDEWEB)
Chen Jie, E-mail: chenjie@bit.edu.c [School of Automation, Beijing Institute of Technology, Beijing, 100081 (China); Sun Jian, E-mail: helios1225@yahoo.com.c [School of Automation, Beijing Institute of Technology, Beijing, 100081 (China); Liu, G.P., E-mail: gpliu@glam.ac.u [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom); CTGT Center in Harbin Institute of Technology, Harbin, 150001 (China); Rees, D., E-mail: drees@glam.ac.u [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom)
2010-09-27
The problem of stability analysis of neural networks with time-varying delay in a given range is investigated in this Letter. By introducing a new Lyapunov functional which uses the information on the lower bound of the delay sufficiently and an augmented Lyapunov functional which contains some triple-integral terms, some improved delay-dependent stability criteria are derived using the free-weighting matrices method. Numerical examples are presented to illustrate the less conservatism of the obtained results and the effectiveness of the proposed method.
Adaptive Fuzzy-Lyapunov Controller Using Biologically Inspired Swarm Intelligence
Directory of Open Access Journals (Sweden)
Alejandro Carrasco Elizalde
2008-01-01
Full Text Available The collective behaviour of swarms produces smarter actions than those achieved by a single individual. Colonies of ants, flocks of birds and fish schools are examples of swarms interacting with their environment to achieve a common goal. This cooperative biological intelligence is the inspiration for an adaptive fuzzy controller developed in this paper. Swarm intelligence is used to adjust the parameters of the membership functions used in the adaptive fuzzy controller. The rules of the controller are designed using a computing-with-words approach called Fuzzy-Lyapunov synthesis to improve the stability and robustness of an adaptive fuzzy controller. Computing-with-words provides a powerful tool to manipulate numbers and symbols, like words in a natural language.
A Lyapunov theory based UPFC controller for power flow control
Energy Technology Data Exchange (ETDEWEB)
Zangeneh, Ali; Kazemi, Ahad; Hajatipour, Majid; Jadid, Shahram [Center of Excellence for Power Systems Automation and Operation, Iran University of Science and Technology, Tehran (Iran)
2009-09-15
Unified power flow controller (UPFC) is the most comprehensive multivariable device among the FACTS controllers. Capability of power flow control is the most important responsibility of UPFC. According to high importance of power flow control in transmission lines, the proper controller should be robust against uncertainty and disturbance and also have suitable settling time. For this purpose, a new controller is designed based on the Lyapunov theory and its stability is also evaluated. The Main goal of this paper is to design a controller which enables a power system to track reference signals precisely and to be robust in the presence of uncertainty of system parameters and disturbances. The performance of the proposed controller is simulated on a two bus test system and compared with a conventional PI controller. The simulation results show the power and accuracy of the proposed controller. (author)
Kick Stability Analysis of the LHC Inflectors
Ducimetière, L; Schröder, G; Vossenberg, Eugène B; Barnes, M J; Wait, G D
1996-01-01
Two sets of four LHC inflector magnet systems must produce a kick of 1.36 Tm each with a duration of 6.5 µs, a rise time of 750 ns, and an overall stability of ± 0.5%. The electrical circuit of the complete system, including all known stray quantities, has been simulated with PSpice. Many stray elements were determined from Opera2D simulations which included eddy-currents. 3D analyses have also been carried out for the kicker magnet using the electromagnetic analysis code Opera3D. Equivalent circuits which simulate the frequency dependence of inductance and resistance of the Pulse Forming Network (PFN) have been derived. The dimensions of the PFN coil have been selected to give the correct pulse response. The end cells of the PFN have also been optimised. The discharge stability of various PFN capacitors has been measured. This paper presents the results of both the analyses and measurements.
Reliability Analysis of Dynamic Stability in Waves
DEFF Research Database (Denmark)
Søborg, Anders Veldt
2004-01-01
exhibit sufficient characteristics with respect to slope at zero heel (GM value), maximum leverarm, positive range of stability and area below the leverarm curve. The rule-based requirements to calm water leverarm curves are entirely based on experience obtained from vessels in operation and recorded......-4 per ship year such brute force Monte-Carlo simulations are not always feasible due to the required computational resources. Previous studies of dynamic stability of ships in waves typically focused on the capsizing event. In this study the objective is to establish a procedure that can identify...... the distribution of the exceedance probability may be established by an estimation of the out-crossing rate of the "safe set" defined by the utility function. This out-crossing rate will be established using the so-called Madsen's Formula. A bi-product of this analysis is a set of short wave time series...
Novel DTA method for thermal stability analysis
Energy Technology Data Exchange (ETDEWEB)
Berty, J.M.; Gandhi, R.J.; Lee, S.
1986-01-01
A Differential Thermal Analysis (DTA) technique to study the kinetics of highly exothermic reactions for estimating thermal stability parameters has been developed. The technique involves measuring and analyzing the heat generated due to the reaction from a differential temperature curve. The technique has been tested by studying the kinetics of the reaction between sodium thiosulfate and hydrogen peroxide whose kinetic parameters are already known and whose thermal stability has been analyzed by a different technique. First the envisiones experiment was simulated on computer, then the DTA experimental equipment was designed on the basis of the computer simulation and finally the actual reaction between Na/sub 2/S/sub 2/O/sub 4/ and H/sub 2/O was performed. The satisfactory results demonstrated the feasibility of the DTA technique for estimating the kinetic parameters.
Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence.
Inubushi, Masanobu; Takehiro, Shin-ichi; Yamada, Michio
2015-08-01
Considering a wall turbulence as a chaotic dynamical system, we study regeneration cycles in a minimal wall turbulence from the viewpoint of orbital instability by employing the covariant Lyapunov analysis developed by [F. Ginelli et al. Phys. Rev. Lett. 99, 130601 (2007)]. We divide the regeneration cycle into two phases and characterize them with the local Lyapunov exponents and the covariant Lyapunov vectors of the Navier-Stokes turbulence. In particular, we show numerically that phase (i) is dominated by instabilities related to the sinuous mode and the streamwise vorticity, and there is no instability in phase (ii). Furthermore, we discuss a mechanism of the regeneration cycle, making use of an energy budget analysis.
Faydasicok, Ozlem; Arik, Sabri
2013-08-01
The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.
Zhang, Xian; Wu, Ligang; Cui, Shaochun
2015-01-01
This paper focuses on stability analysis for a class of genetic regulatory networks with interval time-varying delays. An improved integral inequality concerning on double-integral items is first established. Then, we use the improved integral inequality to deal with the resultant double-integral items in the derivative of the involved Lyapunov-Krasovskii functional. As a result, a delay-range-dependent and delay-rate-dependent asymptotical stability criterion is established for genetic regulatory networks with differential time-varying delays. Furthermore, it is theoretically proven that the stability criterion proposed here is less conservative than the corresponding one in [Neurocomputing, 2012, 93: 19-26]. Based on the obtained result, another stability criterion is given under the case that the information of the derivatives of delays is unknown. Finally, the effectiveness of the approach proposed in this paper is illustrated by a pair of numerical examples which give the comparisons of stability criteria proposed in this paper and some literature.
Stability Analysis of Cohen-Grossberg Neural Networks with Time-Varying Delays
Institute of Scientific and Technical Information of China (English)
LIU Yanqing; TANG Wansheng
2007-01-01
The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential inequality techniques, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of the system are obtained. The criteria do not require the activation functions to be differentiable or monotone nondecreasing. Some stability results from previous works are extended and improved. Comparisons are made to demonstrate the advantage of our results.
The Stability Analysis for an Extended Car Following Model Based on Control Theory
Ge, Hong-Xia; Meng, Xiang-Pei; Zhu, Ke-Qiang; Cheng, Rong-Jun
2014-08-01
A new method is proposed to study the stability of the car-following model considering traffic interruption probability. The stability condition for the extended car-following model is obtained by using the Lyapunov function and the condition for no traffic jam is also given based on the control theory. Numerical simulations are conducted to demonstrate and verify the analytical results. Moreover, numerical simulations show that the traffic interruption probability has an influence on driving behavior and confirm the effectiveness of the method on the stability of traffic flow.
Stability Analysis of Predator-Prey System with Fuzzy Impulsive Control
Directory of Open Access Journals (Sweden)
Yuangan Wang
2012-01-01
Full Text Available Having attracted much attention in the past few years, predator-prey system provides a good mathematical model to present the correlation between predators and preys. This paper focuses on the robust stability of Lotka-Volterra predator-prey system with the fuzzy impulsive control model, and Takagi-Sugeno (T-S fuzzy impulsive control model as well. Via the T-S model and the Lyapunov method, the controlling conditions of the asymptotical stability and exponential stability are established. Furthermore, the numerical simulation for the Lotka-Volterra predator-prey system with impulsive effects verifies the effectiveness of the proposed methods.
Stability Analysis and Stabilization of Miduk Heap Leaching Structure, Iran
Directory of Open Access Journals (Sweden)
Mehdi Amini
2013-06-01
Full Text Available To construct copper heap leaching structures, a stepped heap of ore is placed over an isolated sloping surface and then washed with sulphuric acid. The isolated bed of such a heap consists of some natural and geosynthetic layers. Shear strength parameters between these layers are low, so they form the possible sliding surfaces of the heaps. Economic and environmental considerations call for studying such slides. In this study, firstly, results of the laboratory tests carried on the materials of the heap leaching structures bed are presented. Then, the instability mechanisms of such structures are investigated and proper approaches are summarized for their stabilization. Finally, stability of the Miduk copper heap is evaluated as a case history, and appropriate approaches and their effects are discussed for its stabilization.
Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems
Directory of Open Access Journals (Sweden)
Mircea Lazar
2010-03-01
Full Text Available The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs. Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly reduced compared to classical CLFs, which makes flexible CLFs more suitable for stabilization of constrained discrete-time nonlinear systems and real-time control. The purpose of this overview is to highlight the potential of flexible CLFs for real-time control of fast mechatronic systems, with sampling periods below one millisecond, which are widely employed in aerospace and automotive applications.
On Delay Independent Stabilization Analysis for a Class of Switched Large-Scale Time-Delay Systems
Directory of Open Access Journals (Sweden)
Chi-Jo Wang
2013-01-01
Full Text Available In view of the state-driven switching method, the sufficient stability conditions with delay independence will be derived for the switched large-scale time-delay systems. A new stability criterion of switched large-scale time-delay systems is deduced by Lyapunov stability theorem. The method can be applied to cases when all individual switched systems are unstable. Finally, one example is exploited to illustrate the proposed schemes.
Stability analysis of rubblemound breakwater using ANN
Digital Repository Service at National Institute of Oceanography (India)
Mandal, S.; Rao, S.; Manjunath, Y.R.; Kim, D.H.
are of rubble mound type which consists of one or two layers of heavier armor stones, one or two filter layers consisting of relatively smaller stones and a core of quarry run. The design of the breakwater section, which is normally of a trapezoidal shape... relation is not clear. In more practical terms networks are non-linear modeling tools and they can be used to model complex relationship between input and output system. Earlier applications of neural networks for stability analysis of rubble mound...
Stability analysis of cylindrical Vlasov equilibria
Energy Technology Data Exchange (ETDEWEB)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by cylindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma.
Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice
Tarkhov, Andrei E.; Wimberger, Sandro; Fine, Boris V.
2017-08-01
We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.
Directory of Open Access Journals (Sweden)
Despoina I. Makrygiorgou
2017-03-01
Full Text Available Direct current (DC distribution systems and DC microgrids are becoming a reliable and efficient alternative energy system, compatible with the DC nature of most of the distributed energy resources (DERs, storage devices and loads. The challenging problem of redesigning an autonomous DC-grid system in view of using energy storage devices to balance the power produced and absorbed, by applying simple decentralized controllers on the electronic power interfaces, is investigated in this paper. To this end, a complete nonlinear DC-grid model has been deployed that includes different DC-DERs, two controlled parallel battery branches, and different varying DC loads. Since many loads in modern distribution systems are connected through power converters, both constant power loads and simple resistive loads are considered in parallel. Within this system, suitable cascaded controllers on the DC/DC power converter interfaces to the battery branches are proposed, in a manner that ensures stability and charge sharing between the two branches at the desired ratio. To achieve this task, inner-loop current controllers are combined with outer-loop voltage, droop-based controllers. The proportional-integral (PI inner-loop current controllers include damping terms and are fully independent from the system parameters. The controller scheme is incorporated into the system model and a globally valid nonlinear stability analysis is conducted; this differs from small-signal linear methods that are valid only for specific systems, usually via eigenvalue investigations. In the present study, under the virtual cost of applying advanced Lyapunov techniques on the entire nonlinear system, a rigorous analysis is formulated to prove stability and convergence to the desired operation, regardless of the particular system characteristics. The theoretical results are evaluated by detailed simulations, with the system performance being very satisfactory.
Hydrodynamische Lyapunov-Moden in mehrkomponentigen Lennard-Jones-Flüssigkeiten
Drobniewski, Christian
2011-01-01
Die Charakterisierung hochdimensionaler Systeme mit Lyapunov-Instabilität wird durch das Lyapunov-Spektrum und die zugehörigen Lyapunov-Vektoren ermöglicht. Für eine Vielzahl von derartigen Systemen (Coupled-Map-Lattices, Hartkugel-Systeme, Systeme mit ausgedehnten Potentialen ...) konnte durch die Untersuchung der Lyapunov-Vektoren die Existenz von hydrodynamischen Lyapunov-Moden nachgewiesen werden. Diese kollektiven Anregungen zeigen sich in Lyapunov-Vektoren, deren Lyapunov-Exponenten de...
Adaptive Neural Network Controller for Thermogenerator Angular Velocity Stabilization System
2013-01-01
The paper presents an analytical and simulation approach for the selection of activation functions for the class of neural network controllers for ship’s thermogenerator angular velocity stabilization system. Such systems can be found in many ships. A Lyapunov-like stability analysis is performed in order to obtain a weight update law. A number of simulations were performed to find the best activation function using integral error criteria and statistical T-tests.
Symmetry properties of orthogonal and covariant Lyapunov vectors and their exponents
Posch, Harald A.
2013-06-01
Lyapunov exponents are indicators for the chaotic properties of a classical dynamical system. They are most naturally defined in terms of the time evolution of a set of so-called covariant vectors, co-moving with the linearized flow in tangent space. Taking a simple spring pendulum and the Hénon-Heiles system as examples, we demonstrate the consequences of symplectic symmetry and of time-reversal invariance for such vectors, and study the transformation between different parameterizations of the flow. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.
Dynamic Analysis of Power System Voltage Stability.
Gebreselassie, Assefa
This thesis investigates the effects of loads and voltage regulators on the dynamic voltage stability of power systems. The analysis focuses on the interactions of machine flux dynamics with loads and voltage control devices. The results are based on eigenvalue analysis of the linearized models and time simulation of the nonlinear models, using models from the Power System Toolbox, a Matlab -based package for the simulation and small signal analysis of nonlinear power systems. The voltage stability analysis results are developed using a single machine single load system with typical machine and network parameters and the NPCC 10-machine system. Dynamic models for generators, exciters and loads are used. The generator is modeled with a pair of poles and one damper circuit in both the d-axis and the q-axis. Saturation effects are included in the model. The IEEE Type DC1 DC commutator exciter model is used for all the exciters. Five different types of loads: constant impedance, constant current, constant power, a first order induction motor model (slip model) and a third order induction motor model (slip-flux model) are considered. The modes of instability and the stability limits of the different representation of loads are examined for two different operating modes of the exciters. The first, when all the exciters are on automatic control and the second when some exciters are on manual control. Modal participation factors are used to determine the characteristics of the critical modes. The characteristics of the unstable modes are verified by performing time simulation of the nonlinear models. Oscillatory and non-oscillatory instabilities are experienced by load buses when all the exciters are on automatic control and some exciters are on manual control respectively, for loads which are predominantly constant power and induction motors. It is concluded that the mode of instability does not depend on the type of loads but on the operating condition of the exciters
Nonuniform exponential dichotomies and Lyapunov functions
Barreira, Luis; Dragičević, Davor; Valls, Claudia
2017-05-01
For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
Diverging Fluctuations of the Lyapunov Exponents.
Pazó, Diego; López, Juan M; Politi, Antonio
2016-07-15
We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of suitably correlated background noise.
On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach.
Wang, Zi-Peng; Wu, Huai-Ning
2015-04-01
In this paper, a novel approach to fuzzy sampled-data control of chaotic systems is presented by using a time-dependent Lyapunov functional. The advantage of the new method is that the Lyapunov functional is continuous at sampling times but not necessarily positive definite inside the sampling intervals. Compared with the existing works, the constructed Lyapunov functional makes full use of the information on the piecewise constant input and the actual sampling pattern. In terms of a new parameterized linear matrix inequality (LMI) technique, a less conservative stabilization condition is derived to guarantee the exponential stability for the closed-loop fuzzy sampled-data system. By solving a set of LMIs, the fuzzy sampled-data controller can be easily obtained. Finally, the chaotic Lorenz system and Rössler's system are employed to illustrate the feasibility and effectiveness of the proposed method.
A New Approach to the Method of Lyapunov Functionals and Its Applications
Directory of Open Access Journals (Sweden)
Yunguo Jin
2013-01-01
Full Text Available We show some results which can replace the graph theory used to construct global Lyapunov functions in some coupled systems of differential equations. We present an example of an epidemic model with stage structure and latency spreading in a heterogeneous host population and obtain a more general threshold for the extinction and persistence of a disease. Using some results obtained by mathematical induction and suitable Lyapunov functionals, we prove the global stability of the endemic equilibrium. For some coupled systems of differential equations, by a similar approach to the discussion of the epidemic model, the conditions of threshold property or global stability can be established without the assumption that the relative matrix is irreducible.
On the Stabilization of the Inverted-Cart Pendulum Using the Saturation Function Approach
Directory of Open Access Journals (Sweden)
Carlos Aguilar-Ibañez
2011-01-01
of a well-characterized small vicinity, whereas the second control action asymptotically brings the whole state of the system to the origin. The corresponding closed-loop stability analysis uses standard linear stability arguments as well as the traditional Lyapunov method and the LaSalle's theorem. Our proposed control law ensures global stability of the system in the upper half plane. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
A Stability Criterion for Time-Delay Tension Leg Platform Systems Subjected to External Force
Institute of Scientific and Technical Information of China (English)
Chen-Yuan CHEN; Chien-wen SHEN; Cheng-Wu CHEN; Kevin Fong-Rey LIU; Ming-Jen CHENG
2009-01-01
Stability analysis plays a central role in nonlinear system theory and engineering application.Over the past few yeats,the stability analysis of fuzzy systems has been proposed and there are many successful applications in practical engineering.Therefore,in this paper firstly proposed is the stability analysis on oceanic structure by fuzzy models.In the present study,Takagi-Sugeno (T-S) fuzzy model is proposed for a time delay tension leg platform (TLP) system subjected to an external wave force.In terms of stability analysis,linear matrix inequality (LMI) conditions are derived via Lyapunov theory to guarantee the stability of the TLP system.
Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems
Lazar, M
2010-01-01
The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly ...
Statistics of Lyapunov exponent spectrum in randomly coupled Kuramoto oscillators.
Patra, Soumen K; Ghosh, Anandamohan
2016-03-01
Characterization of spatiotemporal dynamics of coupled oscillatory systems can be done by computing the Lyapunov exponents. We study the spatiotemporal dynamics of randomly coupled network of Kuramoto oscillators and find that the spectral statistics obtained from the Lyapunov exponent spectrum show interesting sensitivity to the coupling matrix. Our results indicate that in the weak coupling limit the gap distribution of the Lyapunov spectrum is Poissonian, while in the limit of strong coupling the gap distribution shows level repulsion. Moreover, the oscillators settle to an inhomogeneous oscillatory state, and it is also possible to infer the random network properties from the Lyapunov exponent spectrum.
Truck Roll Stability Data Collection and Analysis
Energy Technology Data Exchange (ETDEWEB)
Stevens, SS
2001-07-02
The principal objective of this project was to collect and analyze vehicle and highway data that are relevant to the problem of truck rollover crashes, and in particular to the subset of rollover crashes that are caused by the driver error of entering a curve at a speed too great to allow safe completion of the turn. The data are of two sorts--vehicle dynamic performance data, and highway geometry data as revealed by vehicle behavior in normal driving. Vehicle dynamic performance data are relevant because the roll stability of a tractor trailer depends both on inherent physical characteristics of the vehicle and on the weight and distribution of the particular cargo that is being carried. Highway geometric data are relevant because the set of crashes of primary interest to this study are caused by lateral acceleration demand in a curve that exceeds the instantaneous roll stability of the vehicle. An analysis of data quality requires an evaluation of the equipment used to collect the data because the reliability and accuracy of both the equipment and the data could profoundly affect the safety of the driver and other highway users. Therefore, a concomitant objective was an evaluation of the performance of the set of data-collection equipment on the truck and trailer. The objective concerning evaluation of the equipment was accomplished, but the results were not entirely positive. Significant engineering apparently remains to be done before a reliable system can be fielded. Problems were identified with the trailer to tractor fiber optic connector used for this test. In an over-the-road environment, the communication between the trailer instrumentation and the tractor must be dependable. In addition, the computer in the truck must be able to withstand the rigors of the road. The major objective--data collection and analysis--was also accomplished. Using data collected by instruments on the truck, a ''bad-curve'' database can be generated. Using
Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data
Energy Technology Data Exchange (ETDEWEB)
Josiński, Henryk [Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Świtoński, Adam [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland); Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Michalczuk, Agnieszka; Wojciechowski, Konrad [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland)
2015-03-10
The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.
Toropov, A. V.; Toropova, L.V.
2014-01-01
Тhe problem of synthesis of nonlinear speed controller asynchronized switched motor is considered. To find the optimal control law by, the method of Bellman - Lyapunov by concept of "immersion" is used. Modeling and comparative analysis of the system with the standard PI - controller, as well as the synthesized regulators are made
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
STABILITY ANALYSIS OF RIVERBANK SUBJECT TO SEEPAGE
Institute of Scientific and Technical Information of China (English)
Yan LU; Yongjun LU; Xingnong ZHANG
2007-01-01
The stability of riverbanks subject to seepage is studied experimentally and theoretically in this paper. By including seepage in a 3-dimensional theoretical analysis, the study first shows how the critical slope or angle of repose of a cohesionless material is related to the ratio of the hydraulic gradient of seepage to its critical value under the fluidization condition. The critical stable slope is shown to be related to not only the hydraulic gradient but also the seepage direction. Measured laboratory data reasonably fit well with the theoretical relationship for the case of injection and suction. The data reveal that the slope is reduced with injection and increased with suction, respectively. Additionally, the study identifies the seepage direction which results in a minimum critical stable slope for a certain hydraulic gradient of seepage.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
Institute of Scientific and Technical Information of China (English)
M.Syed Ali
2011-01-01
In this paper,the global stability of Takagi-Sugeno(TS)uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays(TSUSFRNNs)is considered.A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs.The proposed stability conditions are demonstrated through numerical examples.Furthermore,the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed.Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.
Institute of Scientific and Technical Information of China (English)
Zhang Hua-Guang; Fu Jie; Ma Tie-Dong; Tong Shao-Cheng
2009-01-01
This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise.Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach,some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties.An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient.Numerical examples are given to illustrate the effectiveness.
The Lyapunov exponents of the Van der Pol oscillator
Grasman, J.; Verhulst, F.; Shih, S.D.
2005-01-01
Lyapunov exponents characterize the dynamics of a system near its attractor. For the Van der Pol oscillator these are quantities for which an approximation should be at hand. Similar to the asymptotic approximation of amplitude and period, expressions are derived for the non-zero Lyapunov exponent
Calculating Lyapunov Exponents: Applying Products and Evaluating Integrals
McCartney, Mark
2010-01-01
Two common examples of one-dimensional maps (the tent map and the logistic map) are generalized to cases where they have more than one control parameter. In the case of the tent map, this still allows the global Lyapunov exponent to be found analytically, and permits various properties of the resulting global Lyapunov exponents to be investigated…
Calculating Lyapunov Exponents: Applying Products and Evaluating Integrals
McCartney, Mark
2010-01-01
Two common examples of one-dimensional maps (the tent map and the logistic map) are generalized to cases where they have more than one control parameter. In the case of the tent map, this still allows the global Lyapunov exponent to be found analytically, and permits various properties of the resulting global Lyapunov exponents to be investigated…
Characterizing heart rate variability by scale-dependent Lyapunov exponent
Hu, Jing; Gao, Jianbo; Tung, Wen-wen
2009-06-01
Previous studies on heart rate variability (HRV) using chaos theory, fractal scaling analysis, and many other methods, while fruitful in many aspects, have produced much confusion in the literature. Especially the issue of whether normal HRV is chaotic or stochastic remains highly controversial. Here, we employ a new multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize HRV. SDLE has been shown to readily characterize major models of complex time series including deterministic chaos, noisy chaos, stochastic oscillations, random 1/f processes, random Levy processes, and complex time series with multiple scaling behaviors. Here we use SDLE to characterize the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects. We show that while HRV data of all these three types are mostly stochastic, the stochasticity is different among the three groups.
FUZZY STABILITY ANALYSIS OF MODE COUPLING CHATTER ON CUTTING PROCESS
Institute of Scientific and Technical Information of China (English)
1998-01-01
The influence of fuzzy uncertainty factors is considered on the analysis of chatter occurring during machine tool cutting process. Using fuzzy mathematics analysis methods, a detailed discussion over fuzzy stability analysis problems is presented related to the mode coupling chatter with respect to intrinsic structure fuzzy factors, and the possibility distribution of the fuzzy stability cutting range and the confidence level expressions of the fuzzy stability cutting width are given.
ANALYSIS AND OPTIMISATION OF DYNAMIC STABILITY OF MOBILE WORKING MACHINES
Directory of Open Access Journals (Sweden)
Peter BIGOŠ
2014-09-01
Full Text Available This paper describes an investigation of the dynamic stability, which is specified for the mobile working machines. There are presented the basic theoretical principles of the stability theory together with an introduction of two illustrative examples of the dynamic stability analysis.
Preparing entangled states by Lyapunov control
Shi, Z. C.; Wang, L. C.; Yi, X. X.
2016-09-01
By Lyapunov control, we present a protocol to prepare entangled states such as Bell states in the context of cavity QED system. The advantage of our method is of threefold. Firstly, we can only control the phase of classical fields to complete the preparation process. Secondly, the evolution time is sharply shortened when compared to adiabatic control. Thirdly, the final state is steady after removing control fields. The influence of decoherence caused by the atomic spontaneous emission and the cavity decay is discussed. The numerical results show that the control scheme is immune to decoherence, especially for the atomic spontaneous emission from |2rangle to |1rangle . This can be understood as the state staying in an invariant subspace. Finally, we generalize this method in preparation of W state.
Preparation of topological modes by Lyapunov control.
Shi, Z C; Zhao, X L; Yi, X X
2015-09-08
By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian. The merit of this control is the individual manipulations on the boundary sites. We take the Kitaev's chain as an illustration for Fermi systems and show that an arbitrary excitation mode can be steered into the Majorana zero mode by manipulating the chemical potential of the boundary sites. For Bose systems, taking the noninteracting Su-Schrieffer-Heeger (SSH) model as an example, we illustrate how to drive the system into the edge mode. The sensitivity of the fidelity to perturbations and uncertainties in the control fields and initial modes is also examined. The experimental feasibility of the proposal and the possibility to replace the continuous control field with square wave pulses is finally discussed.
Preparing entangled states by Lyapunov control
Shi, Z. C.; Wang, L. C.; Yi, X. X.
2016-12-01
By Lyapunov control, we present a protocol to prepare entangled states such as Bell states in the context of cavity QED system. The advantage of our method is of threefold. Firstly, we can only control the phase of classical fields to complete the preparation process. Secondly, the evolution time is sharply shortened when compared to adiabatic control. Thirdly, the final state is steady after removing control fields. The influence of decoherence caused by the atomic spontaneous emission and the cavity decay is discussed. The numerical results show that the control scheme is immune to decoherence, especially for the atomic spontaneous emission from |2rangle to |1rangle . This can be understood as the state staying in an invariant subspace. Finally, we generalize this method in preparation of W state.
Numerical solution of large Lyapunov equations
Saad, Youcef
1989-01-01
A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.
Experimentally realizable control fields in quantum Lyapunov control
Yi, X X; Wu, Chunfeng; Feng, X L; Oh, C H
2011-01-01
As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the system's instantaneous message in the control loop. Often, the Lyapunov control is confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time-delay on the Lyapunov control, and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the controlled system. These results suggest that the Lyapunov control is robust gainst time delay, easy to realize and effective for high-dimensional quantum systems.
Generalized Lyapunov exponent as a unified characterization of dynamical instabilities.
Akimoto, Takuma; Nakagawa, Masaki; Shinkai, Soya; Aizawa, Yoji
2015-01-01
The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent (exponential dynamical instability) is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of nonexponential and exponential dynamical instabilities in one-dimensional maps. Chaos is classified into three different types, i.e., superexponential, exponential, and subexponential chaos. Using one-dimensional maps, we demonstrate superexponential and subexponential chaos and quantify the dynamical instabilities by the Lyapunov pair. In subexponential chaos, we show superweak chaos, which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth. The scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process, which is related to infinite ergodic theory.
Lyapunov exponent diagrams of a 4-dimensional Chua system.
Stegemann, Cristiane; Albuquerque, Holokx A; Rubinger, Rero M; Rech, Paulo C
2011-09-01
We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.
Stability analysis and stabilization of networked linear systems with random packet losses
Institute of Scientific and Technical Information of China (English)
XIE LiHua
2009-01-01
This paper Is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses.Asymptotic stability,mean-square stability,and stochastic stability are considered.For networked discrete-time linear systems,the packet loss period is assumed to be a finite-state Markov chain.We establish that the mean-square stability of a related discrete-time system which evolves in random time Implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time.We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time.For networked sampled-data systems,a binary Markov chain Is used to characterize the packet loss phenomenon of the network.In this case,the packet loss period between two transmission instants is driven by an identically Independently distributed sequence assuming any positive values.Two approaches,namely the Markov jump linear system approach and randomly sampled system approach,are introduced.Based on the stability results derived,we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities.Numerical examples are given to Illustrate the design methods of stabilizing controllers.
Transient Stability Analysis Using Transmission Line Measurement
Institute of Scientific and Technical Information of China (English)
蔡国伟; 程浩忠; 陈家荣; 王承民
2004-01-01
The novel quantitative assessment method using transmission line measurement was developed. A new style of stability criterion was suggested which is based on the line measurement. The stability indices for lines,cutsets and power system according to features of transient energy in the lines were given, which not only provide a reliable and accurate assessment of the transient stability of power system, but also can be used to assess the effect of lines and cutsets on the transient stability and identify the weak transmission segment. Examples were presented by simulation on the IEEE-39 buses test system.
Direct Lyapunov-based control law design for spacecraft attitude maneuvers
Institute of Scientific and Technical Information of China (English)
HU Likun; ANG Qingchao
2006-01-01
A direct Lyapunov-based control law is presented to perform on-orbit stability for spacecraft attitude maneuvers. Spacecraft attitude kinematic equations and dynamic equations are coupled, nonlinear, multi-input multi-output(MIMO), which baffles controller design. Orbit angular rates are taken into account in kinematic equations and influence of gravity gradient moments and disturbance moments on the spacecraft attitude in dynamic equations is considered to approach the practical environment, which enhance the problem complexity to some extent. Based on attitude tracking errors and angular rates, a Lyapunov function is constructed, through which the stabilizing feedback control law is deduced via Lie derivation of the Lyapunov function. The proposed method can deal with the case that the spacecraft is subjected to mass property variations or centroidal inertia matrix variations due to fuel assumption or flexibility, and disturbance moments, which shows the proposed controller is robust for spacecraft attitude maneuvers. The unlimited controller and the limited controller are taken into account respectively in simulations. Simulation results are demonstrated to validate effectiveness and feasibility of the proposed method.
Remarks on boiling water reactor stability analysis. Pt. 2. Stability monitoring
Energy Technology Data Exchange (ETDEWEB)
Lange, Carsten; Hennig, Dieter; Hurtado, Antonio [Technische Univ. Dresden (Germany). Chair of Hydrogen and Nuclear Energy; Schuster, Roland [Kernkraftwerk Brunsbuettel GmbH und Co. oHG, Brunsbuettel (Germany); Lukas, Bernard [EnBW Kernkraft GmbH, Philippsburg (Germany). Kernkraftwerk Philippsburg; Aguirre, Carlos [Kernkraftwerk Leibstadt AG, Aargau (Switzerland)
2012-12-15
In part 1 of this article we explained the partly relative complex solution manifold of the differential equations describing the stability behaviour of a BWR, in particular the coexistence of different types of solutions, such as the coexistence of unstable limit cycles and stable fixed points are of interest from the operational safety point of view. The part 2 is devoted to the surveillance of the stability behaviour. We summarize some stability monitoring methods and suggest to support stability tests by RAM-ROM analyses in order to reveal in advance the stability 'landscape' of the BWR in a parameter region high sensitive for appearing of linear unstable states. The analysis of an especial stability test, performed at NPP Leibstadt (KKL), makes it clear that the measurement results can only be interpreted by application of bifurcation analysis. (orig.)
Cao, Fangfei; Liu, Jinkun
2017-10-01
Considering full state constraints, this paper designs a boundary controller for a two-link rigid-flexible manipulator via Barrier Lyapunov Function. The dynamic model of the two-link rigid-flexible manipulator is described by coupled ordinary differential equations- partial differential equations (ODEs-PDEs). Based on the original model without neglecting the high-frequency modes, boundary controller is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. To ensure that the full state constraints which include position, speed and vibration constraints are not transgressed, a Barrier Lyapunov Function is employed in the proposed controller. The asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle. Simulations are given to verify the effectiveness of the proposed controller with state constraints.
On Designing Lyapunov-Krasovskii Based AQM for Routers Supporting TCP Flows
Labit, Yann; Gouaisbaut, Frédéric; 10.1109/CDC.2007.4434673
2009-01-01
For the last few years, we assist to a growing interest of designing AQM (Active Queue Management) using control theory. In this paper, we focus on the synthesis of an AQM based on the Lyapunov theory for time delay systems. With the help of a recently developed Lyapunov-Krasovskii functional and using a state space representation of a linearized fluid model of TCP, two robust AQMs stabilizing the TCP model are constructed. Notice that our results are constructive and the synthesis problem is reduced to a convex optimization scheme expressed in terms of linear matrix inequalities (LMIs). Finally, an example extracted from the literature and simulations via {\\it NS simulator} support our study.
Liu, Xiaoyang; Yu, Wenwu; Cao, Jinde; Chen, Shun
2015-08-01
This paper is concerned with the sampled-data state estimation and H(∞) filtering for a class of Markovian jump systems with the discontinuous Lyapunov approach. The system measurements are sampled and then transmitted to the estimator and filter in order to estimate the state of the jumped system under consideration. The corresponding error dynamics is represented by a system with two types of delays: one is from the system itself, and the other from the sampling period. As the delay due to sampling is discontinuous, a corresponding discontinuous Lyapunov functional is constructed, and sufficient conditions are established so as to guarantee both the asymptotic mean-square stability and the H(∞) performance for the filtering error systems. The explicit expressions of the desired estimator and filter are further provided. Finally, two simulation examples are given to illustrate the design procedures and performances of the proposed method.
Stochastic stabilization analysis of networked control systems
Institute of Scientific and Technical Information of China (English)
Ma Changlin; Fang Huajing
2007-01-01
Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.
Reliability Analysis of Dynamic Stability in Waves
DEFF Research Database (Denmark)
Søborg, Anders Veldt
2004-01-01
exhibit sufficient characteristics with respect to slope at zero heel (GM value), maximum leverarm, positive range of stability and area below the leverarm curve. The rule-based requirements to calm water leverarm curves are entirely based on experience obtained from vessels in operation and recorded......The assessment of a ship's intact stability is traditionally based on a semi-empirical deterministic concept that evaluates the characteristics of ship's calm water restoring leverarm curves. Today the ship is considered safe with respect to dynamic stability if its calm water leverarm curves...... accidents in the past. The rules therefore only leaves little room for evaluation and improvement of safety of a ship's dynamic stability. A few studies have evaluated the probability of ship stability loss in waves using Monte Carlo simulations. However, since this probability may be in the order of 10...
Solution of the Lyapunov matrix equation for a system with a time-dependent stiffness matrix
DEFF Research Database (Denmark)
Pommer, Christian; Kliem, Wolfhard
2004-01-01
The stability of the linearized model of a rotor system with non-symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces. A disadvantage is nevertheless the occurrenc...... of time-dependent periodic terms in the stiffness matrix. However, by solving the Lyapunov matrix equation we can formulate several stability conditions for the rotor system. Hereby the positive definiteness of a certain averaged stiffness matrix plays a crucial role....
Institute of Scientific and Technical Information of China (English)
Feng Yi-Fu; Zhang Qing-Ling; Feng De-Zhi
2012-01-01
The global stability problem of Takagi-Sugeno (T S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler's lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.
L2-stability of traveling wave solutions to nonlocal evolution equations
Lang, Eva; Stannat, Wilhelm
2016-10-01
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in L2-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum norm. We prove that the linearization around the traveling wave solution satisfies a Lyapunov-type stability condition in a weighted space L2 (ρ) for a naturally associated density ρ. The result can be applied to obtain stability of the traveling wave solution under stochastic perturbations of additive or multiplicative type. For small wave speeds, we also prove an alternative Lyapunov-type stability condition in L2 (m), where m is the symmetrizing density for the traveling wave operator, which allows to derive a long-term stochastic stability result.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection.
Xu, M; Paul, M R
2016-06-01
We explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time-dependent Boussinesq equations for a convection layer in a shallow square box geometry with an aspect ratio of 16 for very long times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. The dynamics explored has fractal dimensions of 20≲D_{λ}≲50, and we compute on the order of 150 covariant Lyapunov vectors. We use the covariant Lyapunov vectors to quantify the degree of hyperbolicity of the dynamics and the degree of Oseledets splitting and to explore the temporal and spatial dynamics of the Lyapunov vectors. Our results indicate that the chaotic dynamics of Rayleigh-Bénard convection is nonhyperbolic for all of the Rayleigh numbers we have explored. Our results yield that the entire spectrum of covariant Lyapunov vectors that we have computed are tangled as indicated by near tangencies with neighboring vectors. A closer look at the spatiotemporal features of the Lyapunov vectors suggests contributions from structures at two different length scales with differing amounts of localization.
M. Syed, Ali
2014-06-01
In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen—Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.
Milling Stability Analysis Based on Chebyshev Segmentation
HUANG, Jianwei; LI, He; HAN, Ping; Wen, Bangchun
2016-09-01
Chebyshev segmentation method was used to discretize the time period contained in delay differential equation, then the Newton second-order difference quotient method was used to calculate the cutter motion vector at each time endpoint, and the Floquet theory was used to determine the stability of the milling system after getting the transfer matrix of milling system. Using the above methods, a two degree of freedom milling system stability issues were investigated, and system stability lobe diagrams were got. The results showed that the proposed methods have the following advantages. Firstly, with the same calculation accuracy, the points needed to represent the time period are less by the Chebyshev Segmentation than those of the average segmentation, and the computational efficiency of the Chebyshev Segmentation is higher. Secondly, if the time period is divided into the same parts, the stability lobe diagrams got by Chebyshev segmentation method are more accurate than those of the average segmentation.
Reliability Analysis of Slope Stability by Central Point Method
Li, Chunge; WU Congliang
2015-01-01
Given uncertainty and variability of the slope stability analysis parameter, the paper proceed from the perspective of probability theory and statistics based on the reliability theory. Through the central point method of reliability analysis, performance function about the reliability of slope stability analysis is established. What’s more, the central point method and conventional limit equilibrium methods do comparative analysis by calculation example. The approach’s numerical ...
Receding horizon control of nonlinear systems: A control Lyapunov function approach
Jadbabaie, Ali
With the advent of faster and cheaper computers, optimization based control methodologies have become a viable candidate for control of nonlinear systems. Over the past twenty years, a group of such control schemes have, been successfully used in the process control industry where the processes are either intrinsically stable or have very large time constants. The purpose of this thesis is to provide a theoretical framework for synthesis of a class of optimization based control schemes, known as receding horizon control techniques for nonlinear systems such as unmanned aerial vehicles. It is well known that unconstrained infinite horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. In this thesis, we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function (CLF). A CLF can be thought of as generalization of the concept of a Lyapunov function to systems with inputs. Roughly speaking, the terminal CLF should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby, relaxing the requirement, that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon
Stability Analysis of an HIV/AIDS Dynamics Model with Drug Resistance
Directory of Open Access Journals (Sweden)
Qianqian Li
2012-01-01
Full Text Available A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance was built in this study. We firstly calculated the threshold value of the basic reproductive number (R0 by the next generation matrix and then analyzed stability of two equilibriums by constructing Lyapunov function. When R0<1, the system was globally asymptotically stable and converged to the disease-free equilibrium. Otherwise, the system had a unique endemic equilibrium which was also globally asymptotically stable. While an antiretroviral drug tried to reduce the infection rate and prolong the patients’ survival, drug resistance was neutralizing the effects of treatment in fact.
Directory of Open Access Journals (Sweden)
Wu Huaiqin
2009-01-01
Full Text Available This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true.
Lyapunov exponents for a Duffing oscillator
Zeni, Andrea R.; Gallas, Jason A. C.
With the help of a parallel computer we perform a systematic computation of Lyapunov exponents for a Duffing oscillator driven externally by a force proportional to cos( t). In contrast to the familiar situation in discrete-time systems where one finds “windows” of regularity embedded in intervals of chaos, we find the continuous-time Duffing oscillator to contain a quite regular epetition of relatively self-similar “islands of chaos” (i.e. regions characterized by positive exponents) embedded in large “seas of regularity” (negative exponents). We also investigate the effect of driving the oscillator with a Jacobian elliptic function cn( t, m). For m = 0 one has cn( t, 0) ≡ cos( t), the usual trigonometric pumping. For m = 1 one has cn( t, 1) ≡ sech( t), a hyperbolic pumping. When 0 displace the islands of chaos in parameter space. Thus, Jacobian pumping provides a possible way of “cleaning chaos” in regions of the parameter space for periodically driven systems.
Random Access Broadcast: Stability and Throughput Analysis
Shrader, Brooke
2007-01-01
A wireless network in which packets are broadcast to a group of receivers through use of a random access protocol is considered in this work. The relation to previous work on networks of interacting queues is discussed and subsequently, the stability and throughput regions of the system are analyzed and presented. A simple network of two source nodes and two destination nodes is considered first. The broadcast service process is analyzed assuming a channel that allows for packet capture and multipacket reception. In this small network, the stability and throughput regions are observed to coincide. The same problem for a network with N sources and M destinations is considered next. The channel model is simplified in that multipacket reception is no longer permitted. Bounds on the stability region are developed using the concept of stability rank and the throughput region of the system is compared to the bounds. Our results show that as the number of destination nodes increases, the stability and throughput reg...
Stability analysis of spacecraft power systems
Halpin, S. M.; Grigsby, L. L.; Sheble, G. B.; Nelms, R. M.
1990-01-01
The problems in applying standard electric utility models, analyses, and algorithms to the study of the stability of spacecraft power conditioning and distribution systems are discussed. Both single-phase and three-phase systems are considered. Of particular concern are the load and generator models that are used in terrestrial power system studies, as well as the standard assumptions of load and topological balance that lead to the use of the positive sequence network. The standard assumptions regarding relative speeds of subsystem dynamic responses that are made in the classical transient stability algorithm, which forms the backbone of utility-based studies, are examined. The applicability of these assumptions to a spacecraft power system stability study is discussed in detail. In addition to the classical indirect method, the applicability of Liapunov's direct methods to the stability determination of spacecraft power systems is discussed. It is pointed out that while the proposed method uses a solution process similar to the classical algorithm, the models used for the sources, loads, and networks are, in general, more accurate. Some preliminary results are given for a linear-graph, state-variable-based modeling approach to the study of the stability of space-based power distribution networks.
Institute of Scientific and Technical Information of China (English)
LI Hong; L(U) Shu; ZHONG Shou-ming
2005-01-01
The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
Institute of Scientific and Technical Information of China (English)
张强; 马润年; 许进
2003-01-01
Global asymptotic stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with continuously distributed delays is studied. Under two mild assumptions on the acti-vation functions, two sufficient conditions ensuring global stability of such networks are derived by utiliz-ing Lyapunov functional and some inequality analysis technique. The results here extend some previous results. A numerical example is given showing the validity of our method.
Global exponential stability of mixed discrete and distributively delayed cellular neural network
Institute of Scientific and Technical Information of China (English)
Yao Hong-Xing; Zhou Jia-Yan
2011-01-01
This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.
Stabilization of a class of discrete-time switched systems via observer-based output feedback
Institute of Scientific and Technical Information of China (English)
Jiao LI; Yuzhong LIU
2007-01-01
In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched. Lyapunov function (SLF) method with Finsler's Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.
Linear stability analysis of supersonic axisymmetric jets
Directory of Open Access Journals (Sweden)
Zhenhua Wan
2014-01-01
Full Text Available Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.
Stability analysis of automobile driver steering control
Allen, R. W.
1981-01-01
In steering an automobile, the driver must basically control the direction of the car's trajectory (heading angle) and the lateral deviation of the car relative to a delineated pathway. A previously published linear control model of driver steering behavior which is analyzed from a stability point of view is considered. A simple approximate expression for a stability parameter, phase margin, is derived in terms of various driver and vehicle control parameters, and boundaries for stability are discussed. A field test study is reviewed that includes the measurement of driver steering control parameters. Phase margins derived for a range of vehicle characteristics are found to be generally consistent with known adaptive properties of the human operator. The implications of these results are discussed in terms of driver adaptive behavior.
Liquefaction mathematical analysis for improvement structures stability
Directory of Open Access Journals (Sweden)
Azam Khodashenas Pelko
2010-10-01
Full Text Available The stability of any structure is possible if foundation is appropriately designed. The Bandar abbas is the largest and most important port of Iran, with high seismicity and occurring strong earthquakes in this territory, the soil mechanical properties of different parts of city have been selected as the subject of current research. The data relating to the design of foundation for improvement of structure at different layer of subsoil have been collected and, accordingly, soil mechanical properties have been evaluated. The results of laboratory experiments can be used for evaluation of geotechnical characteristics of urban area for development a region with high level of structural stability. Ultimately, a new method for calculation of liquefaction force is suggested. It is applicable for improving geotechnical and structure codes and also for reanalysis of structure stability of previously constructed buildings.
Stability Analysis for Stochastic Optimization Problems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
Lyapunov control of quantum systems with impulsive control fields.
Yang, Wei; Sun, Jitao
2013-01-01
We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.
An Analysis of the Stability Pact
Uhlig, H.F.H.V.S.; Beetsma, R.M.W.J.
1997-01-01
We analyse the proposed "Stability Pact" for countries joining a European Monetary Union (EMU). In an EMU shortsighted governments fail to fully internalise the inflationary consequences of their debt policies. This results in excessive debt accumulation. Therefore, while in the absence of EMU gover
Assessment of Stability of Craniofacial Implants by Resonant Frequency Analysis.
Ivanjac, Filip; Konstantinović, Vitomir S; Lazić, Vojkan; Dordević, Igor; Ihde, Stefan
2016-03-01
Implant stability is a principal precondition for the success of implant therapy. Extraoral implants (EO) are mainly used for anchoring of maxillofacial epithesis. However, assessment of implant stability is mostly based on principles derived from oral implants. The aim of this study was to investigate clinical stability of EO craniofacial disk implants (single, double, and triple) by resonance frequency analysis at different stages of the bone's healing. Twenty patients with orbital (11), nasal (5), and auricular (4) defects with 50 EO implants placed for epithesis anchorage were included. Implant stability was measured 3 times; after implant placement, at 3 months and at least after 6 months. A significant increase in implant stability values was noted between all of the measurements, except for triple-disk implants between third and sixth months, and screw implants between 0 and third months. Disk implants showed lower implant stability quotient (ISQ) values compared with screw implants. Triple-disk implants showed better stability compared with single and double-disk implants. Based on resonance frequency analysis values, disk implants could be safely loaded when their ISQ values are 38 (single disks), 47 (double disks), and 48 (triple disks). According to resonance frequency analysis, disk implant stability increased over time, which showed good osseointegration and increasing mineralization. Although EO screw implants showed higher ISQ values than disk implants, disk-type implants can be safely loaded even if lower values of stability are measured.
A Less Conservative Stability Criterion for Delayed Stochastic Genetic Regulatory Networks
Directory of Open Access Journals (Sweden)
Tingting Yu
2014-01-01
Full Text Available This paper concerns the problem of stability analysis for delayed stochastic genetic regulatory networks. By introducing an appropriate Lyapunov-Krasovskii functional and employing delay-range partition approach, a new stability criterion is given to ensure the mean square stability of genetic regulatory networks with time-varying delays and stochastic disturbances. The stability criterion is given in the form of linear matrix inequalities, which can be easily tested by the LMI Toolbox of MATLAB. Moreover, it is theoretically shown that the obtained stability criterion is less conservative than the one in W. Zhang et al., 2012. Finally, a numerical example is presented to illustrate our theory.
Geometry and stability of dynamical systems
Punzi, Raffaele
2008-01-01
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional geometric structure that is not intrinsic to the dynamical system itself. While global Lyapunov stability is based on the choice of seminorms on the vector bundle of perturbations, we propose a definition of local stability based on the choice of a linear connection. We show how this definition reproduces known stability criteria for second order dynamical systems. In contrast to the general case, the special geometry of Lagrangian systems provides completely intrinsic notions of global and local stability. We demonstrate that these do not suffer from the limitations occurring in the analysis of the Maupertuis-Jacobi geodesics associated to natural Lagrangian systems.
Contribution to stability analysis of nonlinear control systems
Directory of Open Access Journals (Sweden)
varc Ivan
2003-12-01
Full Text Available The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The table includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically.Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.
Zamani, Iman; Shafiee, Masoud; Ibeas, Asier
2014-05-01
The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.
Robust stability analysis of singular linear system with delay and parameter uncertainty
Institute of Scientific and Technical Information of China (English)
Renxin ZHONG; Zhi YANG
2005-01-01
This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty.The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed,which is derived by using Lyapunov-Krasovskii functionals,neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result.The robust delay-dependent stability criterion proposed in this paper is a sufficient condition.Finally,numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.
Institute of Scientific and Technical Information of China (English)
HUANG Zhi-Long; JIN Xiao-Ling; ZHU Zi-Qi
2008-01-01
Stability of vertical upright position of an inverted pendulum with its suspension point subjected to high frequency harmonics and stochastic excitations is investigated. Two classes of excitations, i.e., combined high frequency harmonic excitation and Gaussian white noise excitation, and high frequency bounded noise excitation, respectively,are considered. Firstly, the terms of high frequency harmonic excitations in the equation of motion of the system can be set equivalent to nonlinear stiffness terms by using the method of direct separation of motions. Then the stochastic averaging method of energy envelope is used to derive the averaged It(o) stochastic differential equation for system energy. Finally, the stability with probability 1 of the system is studied by using the largest Lyapunov exponent obtained from the averaged It(o) stochastic differential equation. The effects of system parameters on the stability of the system are discussed, and some examples are given to illustrate the efficiency of the proposed procedure.
Huang, Chuangxia; Cao, Jie; Cao, Jinde
2016-10-01
This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations.
Stability analysis of underground engineering based on multidisciplinary design optimization
Institute of Scientific and Technical Information of China (English)
MA Rong; ZHOU Ke-ping; GAO Feng
2008-01-01
Aiming at characteristics of underground engineering,analyzed the feasibility of Multidisciplinary Design Optimization (MDO) used in underground engineering,and put forward a modularization-based MDO method and the idea of MDO to resolve problems in stability analysis,proving the validity and feasibility of using MDO in underground engineering.Characteristics of uncertainty,complexity and nonlinear become bottle-neck to carry on underground engineering stability analysis by MDO.Therefore,the application of MDO in underground engineering stability analysis is still at a stage of exploration,which need some deep research.
Stability analysis of underground engineering based on multidisciplinary design optimization
Institute of Scientific and Technical Information of China (English)
MA Rong; ZHOU Ke-ping; GAO Feng
2008-01-01
Aiming at characteristics of underground engineering, analyzed the feasibility of Multidisciplinary Design Optimization (MDO) used in underground engineering, and put forward a modularization-based MDO method and the idea of MDO to resolve problems in stability analysis, proving the validity and feasibility of using MDO in underground engi-neering. Characteristics of uncertainty, complexity and nonlinear become bottle-neck to carry on underground engineering stability analysis by MDO. Therefore, the application of MDO in underground engineering stability analysis is still at a stage of exploration, which need some deep research.
Application of modern time series analysis to high stability oscillators
Farrell, B. F.; Mattison, W. M.; Vessot, R. F. C.
1980-01-01
Techniques of modern time series analysis useful for investigating the characteristics of high-stability oscillators and identifying systematic perturbations are discussed with reference to an experiment in which the frequencies of superconducting cavity-stabilized oscillators and hydrogen masers were compared. The techniques examined include transformation to stationarity, autocorrelation and cross-correlation, superresolution, and transfer function determination.
Mathematical modelling and linear stability analysis of laser fusion cutting
Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich
2016-06-01
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process' amount of dynamic behavior.
The research analysis and application of stability of ventilation system
Institute of Scientific and Technical Information of China (English)
卢国斌; 陈长华; 葛少成
2002-01-01
The stability of ventilation system includes stabilities of branch, network and main fan. The ventilation system is a dynamic process. The parameters in the ventilation system vary with time. In the paper, a group of mathematical models of quantitative analysis are set up, and the mathematical models are suitable to any ventilation system.
Stability analysis on Jinjia dam hydropower project in Chongqing City
Institute of Scientific and Technical Information of China (English)
Fuzhi XIE; Hong FENG; Xiaohan YANG; Jingzong YU
2006-01-01
The stability analysis is one of the chief problems at hydropower stations. The Jinjia Hydropower Station is a significant project in Southwest China. The paper adopts the rigidity limited equilibrium theory and evaluated stability of the slope body, which will provide the evidences for further detail design.
Stability Analysis for Class of Switched Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; How, Jonathan P.
2010-01-01
Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which...
Performance and stability analysis of a photovoltaic power system
Merrill, W. C.; Blaha, R. J.; Pickrell, R. L.
1978-01-01
The performance and stability characteristics of a 10 kVA photovoltaic power system are studied using linear Bode analysis and a nonlinear analog simulation. Power conversion efficiencies, system stability, and system transient performance results are given for system operation at various levels of solar insolation. Additionally, system operation and the modeling of system components for the purpose of computer simulation are described.
Stability analysis of interacting queues in the ALOHA system
Rao, Ramesh
The author considers the finite-user, infinite-buffer slotted ALOHA system and analytically extends the known bounds for its stability region. The technique used consists of expressing the stability region in terms of certain status probabilities and then solving for the status probabilities by using results from the analysis of dependent queues and that of Markov chains.
G. Chesi
2013-01-01
This paper addresses the problem of establishing robust asymptotical stability of discrete-time systems affected by time-varying parametric uncertainty. Specifically, it is supposed that the coefficients of the system depend linearly on the uncertainty, and that the uncertainty is confined into a polytope. In the continuous-time case, the problem can be addressed by imposing that the system admits a common homogeneous polynomial Lyapunov function (HPLF) at the vertices of the polytope. Unfort...
Stability analysis of dielectric elastomer film actuator
Institute of Scientific and Technical Information of China (English)
LIU YanJu; LIU LiWu; SUN ShouHua; ZHANG Zhen; LENG JinSong
2009-01-01
Dielectric elastomer (DE) is the most promising electroactive polymer material for smart actuators. When a piece of DE film is sandwiched between two compliant electrodes with a high electric field, due to the electrostatic force between the two electrodes, the film expands in-plane and contracts out-of-plane so that its thickness becomes thinner. The thinner thickness results in a higher electric field which inversely squeezes the film again. When the electric field exceeds the critical value, the dielectric field breaks down and the actuator becomes invalid. An elastic strain energy function with two material constants is used to analyze the stability of the dielectric elastomer actuator based on the nonlinear electromechanical field theory. The result shows that the actuator improves its stability as the ratio k of the material constants increases, which can be applied to design of actuators. Finally, this method is extended to study the stability of dielectric elastomers with elastic strain energy functions containing three and more material constants.
Stability analysis of dielectric elastomer film actuator
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Dielectric elastomer (DE) is the most promising electroactive polymer material for smart actuators. When a piece of DE film is sandwiched between two compliant electrodes with a high electric field,due to the electrostatic force between the two electrodes,the film expands in-plane and contracts out-of-plane so that its thickness becomes thinner. The thinner thickness results in a higher electric field which inversely squeezes the film again. When the electric field exceeds the critical value,the dielectric field breaks down and the actuator becomes invalid. An elastic strain energy function with two material constants is used to analyze the stability of the dielectric elastomer actuator based on the nonlinear electromechanical field theory. The result shows that the actuator improves its stability as the ratio k of the material constants increases,which can be applied to design of actuators. Finally,this method is extended to study the stability of dielectric elastomers with elastic strain energy functions containing three and more material constants.
Vector Lyapunov Functions for Stochastic Interconnected Systems
Boussalis, D.
1985-01-01
Theoretical paper presents set of sufficient conditions for asymptotic and exponential stability with probability 1 for class of stochastic interconnected systems. Theory applicable to complicated, large-scale mechanical or electrical systems, and, for several design problems, it reduces computational difficulty by relating stability criteria to fundamental structural features of system.
Vector Lyapunov Functions for Stochastic Interconnected Systems
Boussalis, D.
1985-01-01
Theoretical paper presents set of sufficient conditions for asymptotic and exponential stability with probability 1 for class of stochastic interconnected systems. Theory applicable to complicated, large-scale mechanical or electrical systems, and, for several design problems, it reduces computational difficulty by relating stability criteria to fundamental structural features of system.
Mean flow stability analysis of oscillating jet experiments
Oberleithner, Kilian; Soria, Julio
2014-01-01
Linear stability analysis is applied to the mean flow of an oscillating round jet with the aim to investigate the robustness and accuracy of mean flow stability wave models. The jet's axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry and decomposed into a mean and periodic part utilizing proper orthogonal decomposition. Local linear stability analysis is applied to the measured mean flow adopting a weakly nonparallel flow approach. The resulting global perturbation field is carefully compared to the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pr...
Stability of singular networked control systems with control constraint
Institute of Scientific and Technical Information of China (English)
Qiu Zhanzhi; Zhang Qingling; Zhao Zhiwu
2007-01-01
Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system.Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable.A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.
随机逼近中的Lyapunov函数%On Lyapunov Functions inStochastic Approximation
Institute of Scientific and Technical Information of China (English)
张俊华
2001-01-01
本文研究了随机逼近中满足某种条件的Lyapunov函数的存在性及如何构造Lyapunov函数的问题,讨论了算法收敛性与相应常微分方程系统的渐近稳定性之间的关系.%In this paper, we investigate existence and construction of certain Lyapunov functions instochastic approximation (SA) and discuss the relation between convergence of SA algorithms andasymptotic stability of the corresponding ordinary differential equation systems.
Stability analysis of impulsive functional differential equations
Stamova, Ivanka
2009-01-01
This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equationsis under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied research
Stability Analysis for Regularized Least Squares Regression
Rudin, Cynthia
2005-01-01
We discuss stability for a class of learning algorithms with respect to noisy labels. The algorithms we consider are for regression, and they involve the minimization of regularized risk functionals, such as L(f) := 1/N sum_i (f(x_i)-y_i)^2+ lambda ||f||_H^2. We shall call the algorithm `stable' if, when y_i is a noisy version of f*(x_i) for some function f* in H, the output of the algorithm converges to f* as the regularization term and noise simultaneously vanish. We consider two flavors of...
Truant, Daniel P; Morriss, Gary P
2014-11-01
The covariant Lyapunov analysis is generalized to systems attached to deterministic thermal reservoirs that create a heat current across the system and perturb it away from equilibrium. The change in the Lyapunov exponents as a function of heat current is described and explained. Both the nonequilibrium backward and covariant hydrodynamic Lyapunov modes are analyzed and compared. The movement of the converged angle between the hydrodynamic stable and unstable conjugate manifolds with the free flight time of the dynamics is accurately predicted for any nonequilibrium system simply as a function of their exponent. The nonequilibrium positive and negative LP mode frequencies are found to be asymmetrical, causing the negative mode to oscillate between the two functional forms of each mode in the positive conjugate mode pair. This in turn leads to the angular distributions between the conjugate modes to oscillate symmetrically about π/2 at a rate given by the difference between the positive and negative mode frequencies.
Lyapunov, Floquet, and singular vectors for baroclinic waves
Directory of Open Access Journals (Sweden)
R. M. Samelson
2001-01-01
Full Text Available The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector f1 of the lowest-order unstable periodic orbit over most of the attractor. Departures of the Lyapunov vector from this orientation are primarily rotations of the vector in an approximate tangent plane to the large-scale attractor structure. Exponential growth and decay rates of the Lyapunov vector during individual Poincaré section returns are an order of magnitude larger than the Lyapunov exponent l ≈ 0.016. Relatively large deviations of the Lyapunov vector from parallel to f1 are generally associated with relatively large transient decays. The transient growth and decay of the Lyapunov vector is well described by the transient growth and decay of the leading Floquet vectors of the set of unstable periodic orbits associated with the attractor. Each of these vectors is also nearly parallel to f1. The dynamical splitting of the complete sets of Floquet vectors for the higher-order cycles follows the previous results on the lowest-order cycle, with the vectors divided into wave-dynamical and decaying zonal flow modes. Singular vectors and singular values also generally follow this split. The primary difference between the leading Lyapunov and singular vectors is the contribution of decaying, inviscidly-damped wave-dynamical structures to the singular vectors.
On formalism and stability of switched systems
DEFF Research Database (Denmark)
Leth, John-Josef; Wisniewski, Rafal
2012-01-01
In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differential inclusions, we devise a Lyapunov stability theorem suitable for this class...... of switched systems. With this, we prove a Lyapunov stability theorem for piecewise linear switched systems by means of a concrete class of Lyapunov functions. Contrary to existing results on the subject, the stability theorems in this paper include Filippov (or relaxed) solutions and allow infinite switching...
Modeling, Stability Analysis and Active Stabilization of Multiple DC-Microgrids Clusters
DEFF Research Database (Denmark)
Shafiee, Qobad; Dragicevic, Tomislav; Vasquez, Juan Carlos
2014-01-01
), and more especially during interconnection with other MGs, creating dc MG clusters. This paper develops a small signal model for dc MGs from the control point of view, in order to study stability analysis and investigate effects of CPLs and line impedances between the MGs on stability of these systems......DC microgrids (MGs), as an alternative option, have attracted increasing interest in recent years due to many potential advantages as compare to the ac system. Stability of these systems can be an important issue under high penetration of load converters which behaves as constant power loads (CPLs....... This model can be also used to synthesis and study dynamics of control loops in dc MGs and also dc MG clusters. An active stabilization method is proposed to be implemented as a dc active power filter (APF) inside the MGs in order to not only increase damping of dc MGs at the presence of CPLs but also...
Zhang, Qiumei; Wen, Xiangdan; Jiang, Daqing; Liu, Zhenwen
The present paper deals with the problem of an ecoepidemiological model with linear mass-action functional response perturbed by white noise. The essential mathematical features are analyzed with the help of the stochastic stability, its long time behavior around the equilibrium of deterministic ecoepidemiological model, and the stochastic asymptotic stability by Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.
Simulation analysis of construction process of high rock slope's stabilization
Institute of Scientific and Technical Information of China (English)
ZHU Zhan-yuan; LING Xian-zhang; WANG Xuan-qing; ZOU Zu-yin
2008-01-01
A self-developed elasto-plastic finite element program was used to analyze the construction sequence of high rock slope' s stabilization in a coal-coking plant, and the result was compared with that employing the ultimate equilibrium method. Based on the results of finite element analysis, the stress contour graphs and dis-placement vector graphs at different construction steps were obtained, and the behavior of the slope during stabi-lization construction process was analyzed quantitatively. Based on the analysis of safety factors of three different schemes of stabilization and two different construction schemes, the assessment of stability and bracing design of the construction process were performed. The results show that the original reinforcement design is improper;the stability of the rock slope is controlled by a developed structural plane, the stability factor after excavation is less than 1, and the free surface should be braced in time ; for stability, the construction sequence should adopt that bracing follows excavation step by step up to down; the local slide occurred during the construction process agrees with the dangerous slide determined by the numerical analysis, which proves the validity and rationality of the adopted method.
[A Standing Balance Evaluation Method Based on Largest Lyapunov Exponent].
Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang; Zhao, Qing
2015-12-01
In order to evaluate the ability of human standing balance scientifically, we in this study proposed a new evaluation method based on the chaos nonlinear analysis theory. In this method, a sinusoidal acceleration stimulus in forward/backward direction was forced under the subjects' feet, which was supplied by a motion platform. In addition, three acceleration sensors, which were fixed to the shoulder, hip and knee of each subject, were applied to capture the balance adjustment dynamic data. Through reconstructing the system phase space, we calculated the largest Lyapunov exponent (LLE) of the dynamic data of subjects' different segments, then used the sum of the squares of the difference between each LLE (SSDLLE) as the balance capabilities evaluation index. Finally, 20 subjects' indexes were calculated, and compared with evaluation results of existing methods. The results showed that the SSDLLE were more in line with the subjects' performance during the experiment, and it could measure the body's balance ability to some extent. Moreover, the results also illustrated that balance level was determined by the coordinate ability of various joints, and there might be more balance control strategy in the process of maintaining balance.
Voltage stability analysis in the new deregulated environment
Zhu, Tong
Nowadays, a significant portion of the power industry is under deregulation. Under this new circumstance, network security analysis is more critical and more difficult. One of the most important issues in network security analysis is voltage stability analysis. Due to the expected higher utilization of equipment induced by competition in a power market that covers bigger power systems, this issue is increasingly acute after deregulation. In this dissertation, some selected topics of voltage stability analysis are covered. In the first part, after a brief review of general concepts of continuation power flow (CPF), investigations on various matrix analysis techniques to improve the speed of CPF calculation for large systems are reported. Based on these improvements, a new CPF algorithm is proposed. This new method is then tested by an inter-area transaction in a large inter-connected power system. In the second part, the Arnoldi algorithm, the best method to find a few minimum singular values for a large sparse matrix, is introduced into the modal analysis for the first time. This new modal analysis is applied to the estimation of the point of voltage collapse and contingency evaluation in voltage security assessment. Simulations show that the new method is very efficient. In the third part, after transient voltage stability component models are investigated systematically, a novel system model for transient voltage stability analysis, which is a logical-algebraic-differential-difference equation (LADDE), is offered. As an example, TCSC (Thyristor controlled series capacitors) is addressed as a transient voltage stabilizing controller. After a TCSC transient voltage stability model is outlined, a new TCSC controller is proposed to enhance both fault related and load increasing related transient voltage stability. Its ability is proven by the simulation.
Analysis of lateral stability of I-section aluminum beams
Institute of Scientific and Technical Information of China (English)
CHENG Ming; SHI Yongjiu; WANG Yuanqing
2006-01-01
This paper focuses on the lateral buckling of laterally-unrestrained aluminum beams subjected to a concentrated, uniformly loading and pure-bending action. The design methods of lateral stability of aluminum beams in the current codes are discussed. The influence of material property on the lateral buckling of aluminum beams is investigated with finite element analysis (FEA) methods. Some numerical examples are given, and the results from current codes are compared with the FEA solutions. The design method on lateral stability of steel beams specified in the Chinese standard GB 50017-2003 is modified to calibrate the stability factors of aluminum beams according to the European code, British code, and American code, and the modified method is verified by FEA results. Through comparison with the available test results, the modified design method for overall stability of aluminum bending members is proposed in this paper and proved applicable in the design of lateral stability of aluminum beams.
Stability and robustness analysis of a linear time-periodic system subjected to random perturbations
Redkar, Sangram; Liu, J.; Sinha, S. C.
2012-03-01
In this work, new methods of guaranteeing the stability of linear time periodic dynamical systems with stochastic perturbations are presented. In the approaches presented here, the Lyapunov-Floquet (L-F) transformation is applied first so that the linear time-periodic part of the equations becomes time-invariant. For the linear time periodic system with stochastic perturbations, a stability theorem and related corollary have been suggested using the results previously obtained by Infante. This technique is not only applicable to systems with stochastic parameters but also to systems with deterministic variation in parameters. Some illustrative examples are presented to show the practical applications. These methods can be used to investigate the degree of robustness and design controllers for systems with time periodic coefficients subjected to random perturbations.
Stability Analysis and H∞ Model Reduction for Switched Discrete-Time Time-Delay Systems
Directory of Open Access Journals (Sweden)
Zheng-Fan Liu
2014-01-01
Full Text Available This paper is concerned with the problem of exponential stability and H∞ model reduction of a class of switched discrete-time systems with state time-varying delay. Some subsystems can be unstable. Based on the average dwell time technique and Lyapunov-Krasovskii functional (LKF approach, sufficient conditions for exponential stability with H∞ performance of such systems are derived in terms of linear matrix inequalities (LMIs. For the high-order systems, sufficient conditions for the existence of reduced-order model are derived in terms of LMIs. Moreover, the error system is guaranteed to be exponentially stable and an H∞ error performance is guaranteed. Numerical examples are also given to demonstrate the effectiveness and reduced conservatism of the obtained results.
Modelling and stability analysis of emergent behavior of scalable swarm system
Institute of Scientific and Technical Information of China (English)
CHEN Shi-ming; FANG Hua-jing
2006-01-01
In this paper we propose a two-layer emergent model for scalable swarm system. The first layer describes the individual flocking behavior to the local goal position (the center of minimal circumcircle decided by the neighbors in the positive visual set of individuals) resulting from the individual motion to one or two farthest neighbors in its positive visual set; the second layer describes the emergent aggregating swarm behavior resulting from the individual motion to its local goal position. The scale of the swarm will not be limited because only local individual information is used for modelling in the two-layer topology. We study the stability properties of the swarm emergent behavior based on Lyapunov stability theory. Simulations showed that the swarm system can converge to goal regions while maintaining cohesiveness.
Stability analysis for uncertain switched neural networks with time-varying delay.
Shen, Wenwen; Zeng, Zhigang; Wang, Leimin
2016-11-01
In this paper, stability for a class of uncertain switched neural networks with time-varying delay is investigated. By exploring the mode-dependent properties of each subsystem, all the subsystems are categorized into stable and unstable ones. Based on Lyapunov-like function method and average dwell time technique, some delay-dependent sufficient conditions are derived to guarantee the exponential stability of considered uncertain switched neural networks. Compared with general results, our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being stable, thus getting less conservative criteria. Finally, two numerical examples are provided to show the validity and the advantages of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.
New results on stability analysis for time-varying delay systems with non-linear perturbations.
Liu, Pin-Lin
2013-05-01
The problem of stability for linear time-varying delay systems under nonlinear perturbation is discussed, with delay assumed as time-varying. Delay decomposition approach allows information of the delayed plant states to be fully considered. A less conservative delay-dependent robust stability condition is derived, using integral inequality approach to express the relationship of Leibniz-Newton formula terms in the within the framework of linear matrix inequalities (LMIs). Merits of the proposed results lie in lesser conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and lesser conservatism of the proposed method.
Solar Dynamic Power System Stability Analysis and Control
Momoh, James A.; Wang, Yanchun
1996-01-01
The objective of this research is to conduct dynamic analysis, control design, and control performance test of solar power system. Solar power system consists of generation system and distribution network system. A bench mark system is used in this research, which includes a generator with excitation system and governor, an ac/dc converter, six DDCU's and forty-eight loads. A detailed model is used for modeling generator. Excitation system is represented by a third order model. DDCU is represented by a seventh order system. The load is modeled by the combination of constant power and constant impedance. Eigen-analysis and eigen-sensitivity analysis are used for system dynamic analysis. The effects of excitation system, governor, ac/dc converter control, and the type of load on system stability are discussed. In order to improve system transient stability, nonlinear ac/dc converter control is introduced. The direct linearization method is used for control design. The dynamic analysis results show that these controls affect system stability in different ways. The parameter coordination of controllers are recommended based on the dynamic analysis. It is concluded from the present studies that system stability is improved by the coordination of control parameters and the nonlinear ac/dc converter control stabilize system oscillation caused by the load change and system fault efficiently.
Fully Parallel MHD Stability Analysis Tool
Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang
2015-11-01
Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.
Kinematic analysis of rope skipper's stability
Ab Ghani, Nor Atikah; Rambely, Azmin Sham
2014-06-01
There are various kinds of jumping that can be done while performing rope skipping activity. This activity was always associated with injury. But, if the rope skipper can perform the activity in a right way, it is believed that the injury might be reduced. The main purpose of this paper is to observe the stability of rope skipper from a biomechanics perspective, which are the centre of mass, angle at the ankle, knee and hip joints and also the trajectory for the ipsilateral leg between the two types of skip which is one leg and two legs. Six healthy, physically active subject, two males and four females (age: 8.00±1.25 years, weight: 17.90±6.85 kg and height: 1.22±0.08 m) participated in this study. Kinematic data of repeated five cycles of rope skipping activity was captured by using Vicon Nexus system. Based on the data collected, skipping with two legs shows more stable behavior during preparation, flight and landing phases. It is concluded that landing on the balls of the feet, lowering the trajectory positions of the feet from the ground as well as flexion of each joint which would reduce the injury while landing.
Stability analysis for natural slope by kinematical approach
Institute of Scientific and Technical Information of China (English)
孙志彬; 覃长兵
2014-01-01
The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ (N) using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C(1) maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
On Controllability and Observability of Fuzzy Dynamical Matrix Lyapunov Systems
Directory of Open Access Journals (Sweden)
M. S. N. Murty
2008-04-01
Full Text Available We provide a way to combine matrix Lyapunov systems with fuzzy rules to form a new fuzzy system called fuzzy dynamical matrix Lyapunov system, which can be regarded as a new approach to intelligent control. First, we study the controllability property of the fuzzy dynamical matrix Lyapunov system and provide a sufficient condition for its controllability with the use of fuzzy rule base. The significance of our result is that given a deterministic system and a fuzzy state with rule base, we can determine the rule base for the control. Further, we discuss the concept of observability and give a sufficient condition for the system to be observable. The advantage of our result is that we can determine the rule base for the initial value without solving the system.
Characterizing weak chaos using time series of Lyapunov exponents.
da Silva, R M; Manchein, C; Beims, M W; Altmann, E G
2015-06-01
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite-time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semiordered (or semichaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase space associated to them. Applying our methodology to a chain of coupled standard maps we obtain (i) that it allows for an improved numerical characterization of stickiness in high-dimensional Hamiltonian systems, when compared to the previous analyses based on the distribution of recurrence times; (ii) that the transition probabilities between different regimes are determined by the phase-space volume associated to the corresponding regions; and (iii) the dependence of the Lyapunov exponents with the coupling strength.
Lyapunov exponents for synchronous 12-lead ECG signals
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The Lyapunov exponents of synchronous 12-lead ECG signals have been investigated for the first time using a multi-sensor (electrode) technique. The results show that the Lyapunov exponents computed from different locations on the body surface are not the same, but have a distribution characteristic for the ECG signals recorded from coronary artery disease (CAD) patients with sinus rhythms and for signals from healthy older people. The maximum Lyapunov exponent L1 of all signals is positive. While all the others are negative, so the ECG signal has chaotic characteristics. With the same leads, L1 of CAD patients is less than that of healthy people, so the CAD patients and healthy people can be classified by L1, L1 therefore has potential values in the diagnosis of heart disease.
Lyapunov exponents of stochastic systems—from micro to macro
Laffargue, Tanguy; Tailleur, Julien; van Wijland, Frédéric
2016-03-01
Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the ‘same noise realization’. The purpose of this work is to critically examine what this expression means. For Brownian particles, we consider two natural interpretations of the noise: intrinsic to the particles or stemming from the fluctuations of the environment. We show how they lead to different distributions of the largest Lyapunov exponent as well as different fluctuating hydrodynamics for the collective density field. We discuss, both at microscopic and macroscopic levels, the limits in which these noise prescriptions become equivalent. We close this paper by providing an estimate of the largest Lyapunov exponent and of its fluctuations for interacting particles evolving with Dean-Kawasaki dynamics.
Fazanaro, Filipe I; Soriano, Diogo C; Suyama, Ricardo; Attux, Romis; Madrid, Marconi K; de Oliveira, José Raimundo
2013-06-01
The present work aims to apply a recently proposed method for estimating Lyapunov exponents to characterize-with the aid of the metric entropy and the fractal dimension-the degree of information and the topological structure associated with multiscroll attractors. In particular, the employed methodology offers the possibility of obtaining the whole Lyapunov spectrum directly from the state equations without employing any linearization procedure or time series-based analysis. As a main result, the predictability and the complexity associated with the phase trajectory were quantified as the number of scrolls are progressively increased for a particular piecewise linear model. In general, it is shown here that the trajectory tends to increase its complexity and unpredictability following an exponential behaviour with the addition of scrolls towards to an upper bound limit, except for some degenerated situations where a non-uniform grid of scrolls is attained. Moreover, the approach employed here also provides an easy way for estimating the finite time Lyapunov exponents of the dynamics and, consequently, the Lagrangian coherent structures for the vector field. These structures are particularly important to understand the stretching/folding behaviour underlying the chaotic multiscroll structure and can provide a better insight of phase space partition and exploration as new scrolls are progressively added to the attractor.
Stability Criteria for Large-Scale Linear Systems with Structured Uncertainties
Institute of Scientific and Technical Information of China (English)
Cao Dengqing
1996-01-01
The robust stability analysis for large-scale linear systems with structured timevarying uncertainties is investigated in this paper. By using the scalar Lyapunov functions and the properties of M-matrix and nonnegative matrix, stability robustness measures are proposed. The robust stability criteria obtained are applied to derive an algebric criterion which is expressed directly in terms of plant parameters and is shown to be less conservative than the existing ones. A numerical example is given to demonstrate the stability criteria obtained and to compare them with the previous ones.
THE STABILITY IN NEURAL NETWORK WITH DELAY AND DYNAMICAL THRESHOLD EFFECTS%具有时滞与动态阈值的神经网络模型中的稳定性
Institute of Scientific and Technical Information of China (English)
钟文勇; 林伟; 阮炯
2001-01-01
In this paper, sufficient conditions are derived for the globally asymptotical stability of the equilibrium in a kind of differential equation with delay originally from modeling the action of a neuron with dynamical threshold effects. Both strict analysis concerns with Lyapunov functional and Computer simulation are given in this paper.Furthermore, we generalize the results in the higher-dimensional equations.
Lyapunov based nonlinear control of electrical and mechanical systems
Behal, Aman
This Ph.D. dissertation describes the design and implementation of various control strategies centered around the following applications: (i) an improved indirect field oriented controller for the induction motor, (ii) partial state feedback control of an induction motor with saturation effects, (iii) tracking control of an underactuated surface vessel, and (iv) an attitude tracking controller for an underactuated spacecraft. The theory found in each of these sections is demonstrated through simulation or experimental results. An introduction to each of these four primary chapters can be found in chapter one. In the second chapter, the previously published tracking control of [16] 1 is presented in the indirect field oriented control (IFOC) notation to achieve exponential rotor velocity/rotor flux tracking. Specifically, it is illustrated how the proposed IFOC controller can be rewritten in the manner of [16] to allow for a direct Lyapunov stability proof. Experimental results (implemented with the IFOC algorithm) are provided to corroborate the efficacy of the algorithm. In the third chapter, a singularity-free, rotor position tracking controller is presented for the full order, nonlinear dynamic model of the induction motor that includes the effects of magnetic saturation. Specifically, by utilizing the pi-equivalent saturation model, an observer/controller strategy is designed that achieves semi-global exponential rotor position tracking and only requires stator current, rotor velocity, and rotor position measurements. Simulation and experimental results are included to demonstrate the efficacy of the proposed algorithm. In the fourth chapter, a continuous, time-varying tracking controller is designed that globally exponentially forces the position/orientation tracking error of an under-actuated surface vessel to a neighborhood about zero that can be made arbitrarily small (i.e., global uniformly ultimately boundedness (GUUB)). The result is facilitated by
Baba, Isa Abdullahi; Hincal, Evren
2017-05-01
In this article we studied an epidemic model consisting of two strains with different types of incidence rates; bilinear and non-monotone. The model consists of four equilibrium points: disease-free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R 1 0 and R 2 0 are found, and we have shown that if both are less than one, the disease dies out, and if both are greater than one epidemic occurs. Furthermore, epidemics occur with respect to any strain with a basic reproduction ratio greater than one and disease dies out with respect to any strain with a basic reproduction ratio less than one. It was also shown that any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Numerical simulations were carried out to support the analytic result and to show the effect of the parameter k in the non-monotone incidence rate, which describes the psychological effect of general public towards infection.
Lyapunov exponents for multi-parameter tent and logistic maps.
McCartney, Mark
2011-12-01
The behaviour of logistic and tent maps is studied in cases where the control parameter is dependent on iteration number. Analytic results for global Lyapunov exponent are presented in the case of the tent map and numerical results are presented in the case of the logistic map. In the case of a tent map with N control parameters, the fraction of parameter space for which the global Lyapunov exponent is positive is calculated. The case of bi-parameter maps of period N are investigated.
An iterative decoupling solution method for large scale Lyapunov equations
Athay, T. M.; Sandell, N. R., Jr.
1976-01-01
A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.
Do Finite-Size Lyapunov Exponents detect coherent structures?
Karrasch, Daniel; Haller, George
2013-12-01
Ridges of the Finite-Size Lyapunov Exponent (FSLE) field have been used as indicators of hyperbolic Lagrangian Coherent Structures (LCSs). A rigorous mathematical link between the FSLE and LCSs, however, has been missing. Here, we prove that an FSLE ridge satisfying certain conditions does signal a nearby ridge of some Finite-Time Lyapunov Exponent (FTLE) field, which in turn indicates a hyperbolic LCS under further conditions. Other FSLE ridges violating our conditions, however, are seen to be false positives for LCSs. We also find further limitations of the FSLE in Lagrangian coherence detection, including ill-posedness, artificial jump-discontinuities, and sensitivity with respect to the computational time step.
Lyapunov spectra of Coulombic and gravitational periodic systems
Kumar, Pankaj
2016-01-01
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward computing Lypaunov characteristic exponents using an event-driven algorithm. The results indicate that the energy dependence of the largest Lyapunov exponent emulates that of Kolmogorov-entropy density for each system at different degrees of freedom. Our approach forms an effective and approximation-free tool toward studying the dynamical properties exhibited by the Coulombic and gravitational systems and finds applications in investigating indications of thermodynamic transitions in large versions of the spatially periodic systems.
An iterative decoupling solution method for large scale Lyapunov equations
Athay, T. M.; Sandell, N. R., Jr.
1976-01-01
A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.
Fan, Xiaofei; Zhang, Xian; Wu, Ligang; Shi, Michael
2017-01-01
This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.
Shah, Neerav
2011-01-01
The Magnetospheric MultiScale Mission (MMS) is scheduled to launch in late 2014. Its primary goal is to discover the fundamental plasma physics processes of reconnection in the Earth's magnetosphere. Each of the four MMS spacecraft is spin-stabilized at a nominal rate of 3 RPM. Traditional spin-stabilized spacecraft have used a number of separate modes to control nutation, spin rate, and precession. To reduce the number of modes and simplify operations, the Delta-H control mode is designed to accomplish nutation control, spin rate control, and precession control simultaneously. A nonlinear design technique, Lyapunov's method, is used to design the Delta-H control mode. A global spin rate controller selected as the baseline controller for MMS, proved to be insufficient due to an ambiguity in the attitude. Lyapunov's design method was used to solve this ambiguity, resulting in a controller that meets the design goals. Simulation results show the advantage of the pointing and rate controller for maneuvers larger than 90 deg and provide insight into the performance of this controller.
Stability Analysis for a Multi-Camera Photogrammetric System
Directory of Open Access Journals (Sweden)
Ayman Habib
2014-08-01
Full Text Available Consumer-grade digital cameras suffer from geometrical instability that may cause problems when used in photogrammetric applications. This paper provides a comprehensive review of this issue of interior orientation parameter variation over time, it explains the common ways used for coping with the issue, and describes the existing methods for performing stability analysis for a single camera. The paper then points out the lack of coverage of stability analysis for multi-camera systems, suggests a modification of the collinearity model to be used for the calibration of an entire photogrammetric system, and proposes three methods for system stability analysis. The proposed methods explore the impact of the changes in interior orientation and relative orientation/mounting parameters on the reconstruction process. Rather than relying on ground truth in real datasets to check the system calibration stability, the proposed methods are simulation-based. Experiment results are shown, where a multi-camera photogrammetric system was calibrated three times, and stability analysis was performed on the system calibration parameters from the three sessions. The proposed simulation-based methods provided results that were compatible with a real-data based approach for evaluating the impact of changes in the system calibration parameters on the three-dimensional reconstruction.
Probabilistic approaches for geotechnical site characterization and slope stability analysis
Cao, Zijun; Li, Dianqing
2017-01-01
This is the first book to revisit geotechnical site characterization from a probabilistic point of view and provide rational tools to probabilistically characterize geotechnical properties and underground stratigraphy using limited information obtained from a specific site. This book not only provides new probabilistic approaches for geotechnical site characterization and slope stability analysis, but also tackles the difficulties in practical implementation of these approaches. In addition, this book also develops efficient Monte Carlo simulation approaches for slope stability analysis and implements these approaches in a commonly available spreadsheet environment. These approaches and the software package are readily available to geotechnical practitioners and alleviate them from reliability computational algorithms. The readers will find useful information for a non-specialist to determine project-specific statistics of geotechnical properties and to perform probabilistic analysis of slope stability.
Pyrosequencing Based Microbial Community Analysis of Stabilized Mine Soils
Park, J. E.; Lee, B. T.; Son, A.
2015-12-01
Heavy metals leached from exhausted mines have been causing severe environmental problems in nearby soils and groundwater. Environmental mitigation was performed based on the heavy metal stabilization using Calcite and steel slag in Korea. Since the soil stabilization only temporarily immobilizes the contaminants to soil matrix, the potential risk of re-leaching heavy metal still exists. Therefore the follow-up management of stabilized soils and the corresponding evaluation methods are required to avoid the consequent contamination from the stabilized soils. In this study, microbial community analysis using pyrosequencing was performed for assessing the potential leaching of the stabilized soils. As a result of rarefaction curve and Chao1 and Shannon indices, the stabilized soil has shown lower richness and diversity as compared to non-contaminated negative control. At the phyla level, as the degree of contamination increases, most of phyla decreased with only exception of increased proteobacteria. Among proteobacteria, gamma-proteobacteria increased against the heavy metal contamination. At the species level, Methylobacter tundripaludum of gamma-proteobacteria showed the highest relative portion of microbial community, indicating that methanotrophs may play an important role in either solubilization or immobilization of heavy metals in stabilized soils.
ANALYSIS OF TIPOVER STABILITY FOR NOVEL SHAPE SHIFTING MODULAR ROBOT
Institute of Scientific and Technical Information of China (English)
LIU Jinguo; WANG Yuechao; MA Shugen; LI Bin
2006-01-01
A novel three-module robot has been introduced. It can change its configuration toadapt to the uneven terrain and to improve its tipover stability. This three-module tracked robot has three kinds of symmetry configuration. They are line type, triangle type, and row type. After the factors and the countermeasures of mobile robot's tipover problem are analyzed, stability pyramid and tipover stability index are proposed to globally determinate the mobile robot's static stability and dynamic stability.The shape shifting robot is tested by this technique under the combined disturbance of pitch, roll and yaw in simulation. The simulation result shows that this technique is effective for the analysis of mobile robot's tipover stability, especially for the reconfigurable or shape shifting modular robot.Experiments on three symmetry configurations are made under unstructured environments. The environment experiment shows the same result as that of the simulation that the triangle type configuration has the best stability. Both simulation and experiment provide a valid reference for the reconfigurable robot's potential application.
Stability analysis of an encapsulated microbubble against gas diffusion.
Katiyar, Amit; Sarkar, Kausik
2010-03-01
Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although bubbles, containing gases other than air, are considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support a net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided.
Matrix properties relating to stability analysis
Energy Technology Data Exchange (ETDEWEB)
Di Caprio, U. [ENEL s.p.a., Cologno Monzese (Italy)
2001-03-01
With reference to a multimachine power system are presented properties and conditions to be satisfied by matrices M, K, D (inertia coefficients, synchronizing coefficients and damping coefficients) in order that the system can be stable. The analysis is carried out with the assumption that the transfer-conductances are negligible while the damping effects (of the field and damper circuits) are taken into account. The formulation is general, i.e. it can be applied to any system with n degrees of freedom, subjected to conservative positional forces and to dissipative forces linearly dependent upon the speed. (author)
Stability analysis of an aeroelastic system with friction
Institute of Scientific and Technical Information of China (English)
Tan Tiancai; Li Min; Liu Baihui
2013-01-01
In this paper,harmonic balance method,exact formulation and numerical simulation method are adopted to study the effects of different friction stiffness on the stability of 1.5 degrees of freedom aeroelastic system.On this basis,the expressions of input energy and dissipated energy are deduced,and the energy method is used to reveal the mechanisms of the stable boundary and unstable boundary existing in the system and the effects of different friction stiffness on the stability of the system.Studies have shown that the stability region and the critical aerodynamic damping ratio of the system rise with the increase of the friction stiffness,while the friction stiffness has little effect on the stability boundary.In the analysis of the stability of system,the results of harmonic balance method,exact formulation and Newmark of numerical simulation method are in good agreement.Compared with exact formulation and numerical simulation method,the concept and conclusion of harmonic balance method are simple in the system stability analysis.
Static Voltage Stability Analysis by Using SVM and Neural Network
Directory of Open Access Journals (Sweden)
Mehdi Hajian
2013-01-01
Full Text Available Voltage stability is an important problem in power system networks. In this paper, in terms of static voltage stability, and application of Neural Networks (NN and Supported Vector Machine (SVM for estimating of voltage stability margin (VSM and predicting of voltage collapse has been investigated. This paper considers voltage stability in power system in two parts. The first part calculates static voltage stability margin by Radial Basis Function Neural Network (RBFNN. The advantage of the used method is high accuracy in online detecting the VSM. Whereas the second one, voltage collapse analysis of power system is performed by Probabilistic Neural Network (PNN and SVM. The obtained results in this paper indicate, that time and number of training samples of SVM, are less than NN. In this paper, a new model of training samples for detection system, using the normal distribution load curve at each load feeder, has been used. Voltage stability analysis is estimated by well-know L and VSM indexes. To demonstrate the validity of the proposed methods, IEEE 14 bus grid and the actual network of Yazd Province are used.
Performance and Stability Analysis of a Shrouded-Fan UAV
de Divitiis, Nicola
2009-01-01
This paper deals with the estimation of the performance and stability for a shrouded-fan unmanned rotorcraft whose mission profile also prescribes the flight in ground effect. The not so simple estimation of the aerodynamic coefficients and of the thrust in the various situations makes the performance calculation and the stability analysis difficult tasks. This is due to the strong interaction between the fan flow and shroud that causes quite different flow structures about the airframe depending on flight conditions. A further difficulty is related to the ground effect which produces substantial modifications in the rotor thrust and aerodynamic coefficients. To evaluate performance and stability, two models have been developed. One determines the aerodynamic coefficients of the shroud, whereas the other one calculates thrust and moment of the rotors system. Both models take into account the mutual interference between fan flow and fuselage and ground effect. Performance and stability are then discussed with ...
Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method
Directory of Open Access Journals (Sweden)
Seval Pinarbasi
2012-01-01
Full Text Available The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method (HPM.
Power system small signal stability analysis and control
Mondal, Debasish; Sengupta, Aparajita
2014-01-01
Power System Small Signal Stability Analysis and Control presents a detailed analysis of the problem of severe outages due to the sustained growth of small signal oscillations in modern interconnected power systems. The ever-expanding nature of power systems and the rapid upgrade to smart grid technologies call for the implementation of robust and optimal controls. Power systems that are forced to operate close to their stability limit have resulted in the use of control devices by utility companies to improve the performance of the transmission system against commonly occurring power system
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
Institute of Scientific and Technical Information of China (English)
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
EVENTUAL STABILITY OF IMPULSIVE DIFFERENTIAL SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this article, criteria of eventual stability are established for impulsive differential systems using piecewise continuous Lyapunov functions. The sufficient conditions that are obtained significantly depend on the moments of impulses. An example is discussed to illustrate the theorem.
Orbital stability analysis and chaotic dynamics of exoplanets in multi-stellar systems
Satyal, Suman
The advancement in detection technology has substantially increased the discovery rate of exoplanets in the last two decades. The confirmation of thousands of exoplanets orbiting the solar type stars has raised new astrophysical challenges, including the studies of orbital dynamics and long-term stability of such planets. Continuous orbital stability of the planet in stellar habitable zone is considered vital for life to develop. Hence, these studies furthers one self-evident aim of mankind to find an answer to the century old question: Are we alone?. This dissertation investigates the planetary orbits in single and binary star systems. Within binaries, a planet could orbit either one or both stars as S-type or P-type, respectively. I have considered S-type planets in two binaries, gamma Cephei and HD 196885, and compute their orbits by using various numerical techniques to assess their periodic, quasi-periodic or chaotic nature. The Hill stability (HS) function, which measures the orbital perturbation induced by the nearby companion, is calculated for each system and then its efficacy as a new chaos indicator is tested against Maximum Lyapunov Exponents (MLE) and Mean Exponential Growth factor of Nearby Orbits (MEGNO). The dynamics of HD 196885 AB is further explored with an emphasis on the planet's higher orbital inclination relative to the binary plane. I have quantitatively mapped out the chaotic and quasi-periodic regions of the system's phase space, which indicates a likely regime of the planet's inclination. In, addition, the resonant angle is inspected to determine whether alternation between libration and circulation occurs as a consequence of Kozai oscillations, a probable mechanism that can drive the planetary orbit to a large inclination. The studies of planetary system in GJ 832 shows potential of hosting multiple planets in close orbits. The phase space of GJ 832c (inner planet) and the Earth-mass test planet(s) are analyzed for periodic
Global stabilization of nonlinear systems with uncertain structure
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
Surficial Stability Analysis for Landslide Prediction
Cho, Sung Eun
2017-04-01
In Korea where rainfall of strong intensities is frequent, the depth of weathered residual soil is shallow in mountainous region. Therefore, full saturation of soil layer caused by the reaching of rainwater from the slope surface to impermeable bedrock is one of important causes of landslide. In this study, a shallow slope failure analysis method for slopes with shallow bedrock was developed to predict landslide based on one-dimensional Green-Ampt model. Constant intensities of rainfall were considered and shallow impermeable boundary condition was imposed on the Green-Ampt model to simulate the impermeable bedrock underlying the shallow weathered residual soil. The prediction results showed that the proposed method can be used to predict the landslide due to rainfall infiltration by efficiently considering the movement of the saturated region in the hillslope with shallow impermeable bedrock. Acknowledgements This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2012M3A2A1050981).
Black tea: chemical analysis and stability.
Li, Shiming; Lo, Chih-Yu; Pan, Min-Hsiung; Lai, Ching-Shu; Ho, Chi-Tang
2013-01-01
Tea is the most popular flavored and functional drink worldwide. The nutritional value of tea is mostly from the tea polyphenols that are reported to possess a broad spectrum of biological activities, including anti-oxidant properties, reduction of various cancers, inhibition of inflammation, and protective effects against diabetes, hyperlipidemia and obesity. Tea polyphenols include catechins and gallic acid in green and white teas, and theaflavins and thearubigins as well as other catechin polymers in black and oolong teas. Accurate analysis of black tea polyphenols plays a significant role in the identification of black tea contents, quality control of commercial tea beverages and extracts, differentiation of various contents of theaflavins and catechins and correlations of black tea identity and quality with biological activity, and most importantly, the establishment of the relationship between quantitative tea polyphenol content and its efficacy in animal or human studies. Global research in tea polyphenols has generated much in vitro and in vivo data rationally correlating tea polyphenols with their preventive and therapeutic properties in human diseases such as cancer, and metabolic and cardiovascular diseases etc. Based on these scientific findings, numerous tea products have been developed including flavored tea drinks, tea-based functional drinks, tea extracts and concentrates, and dietary supplements and food ingredients, demonstrating the broad applications of tea and its extracts, particularly in the field of functional food.
Reliability analysis method for slope stability based on sample weight
Directory of Open Access Journals (Sweden)
Zhi-gang YANG
2009-09-01
Full Text Available The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method (FEM, may not include some important information, especially for steep slopes with complex geological conditions. This paper presents a new reliability method that uses sample weight analysis. Based on the distribution characteristics of random variables, the minimal sample size of every random variable is extracted according to a small sample t-distribution under a certain expected value, and the weight coefficient of each extracted sample is considered to be its contribution to the random variables. Then, the weight coefficients of the random sample combinations are determined using the Bayes formula, and different sample combinations are taken as the input for slope stability analysis. According to one-to-one mapping between the input sample combination and the output safety coefficient, the reliability index of slope stability can be obtained with the multiplication principle. Slope stability analysis of the left bank of the Baihetan Project is used as an example, and the analysis results show that the present method is reasonable and practicable for the reliability analysis of steep slopes with complex geological conditions.
A conjecture on the norm of Lyapunov mapping
Institute of Scientific and Technical Information of China (English)
Daizhan CHENG; Yahong ZHU; Hongsheng QI
2009-01-01
A conjecture that the norm of Lyapunov mapping LA equals to its restriction to the symmetric set,S,i.e.,‖LA‖ = ‖LA |s‖ was proposed in [1].In this paper,a method for numerical testing is provided first.Then,some recent progress on this conjecture is presented.
Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales
Institute of Scientific and Technical Information of China (English)
ZHANG JI; LIU ZHEN-XIN
2011-01-01
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△ ＝ A(t)x on time scales.Moreover, for the nonlinear perturbed equation x△ ＝ A(t)x + f(t,x) we give the instability of the zero solution when f is sufficiently small.
Alignment of Lyapunov Vectors: A Quantitative Criterion to Predict Catastrophes?
Beims, Marcus W; Gallas, Jason A C
2016-11-15
We argue that the alignment of Lyapunov vectors provides a quantitative criterion to predict catastrophes, i.e. the imminence of large-amplitude events in chaotic time-series of observables generated by sets of ordinary differential equations. Explicit predictions are reported for a Rössler oscillator and for a semiconductor laser with optoelectronic feedback.
Alignment of Lyapunov Vectors: A Quantitative Criterion to Predict Catastrophes?
Beims, Marcus W.; Gallas, Jason A. C.
2016-11-01
We argue that the alignment of Lyapunov vectors provides a quantitative criterion to predict catastrophes, i.e. the imminence of large-amplitude events in chaotic time-series of observables generated by sets of ordinary differential equations. Explicit predictions are reported for a Rössler oscillator and for a semiconductor laser with optoelectronic feedback.
The Lyapunov exponents of C~1 hyperbolic systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Let f be a C 1 diffeomorphisim of smooth Riemannian manifold and preserve a hyperbolic ergodic measure μ. We prove that if the Osledec splitting is dominated, then the Lyapunov exponents of μ can be approximated by the exponents of atomic measures on hyperbolic periodic orbits.
Lyapunov exponents and particle dispersion in drift wave turbulence
DEFF Research Database (Denmark)
Pedersen, T.S.; Michelsen, Poul; Juul Rasmussen, J.
1996-01-01
The Hasegawa-Wakatani model equations for resistive drift waves are solved numerically for a range of values of the coupling due to the parallel electron motion. The largest Lyapunov exponent, lambda(1), is calculated to quantify the unpredictability of the turbulent flow and compared to other...
From Lyapunov modes to their exponents for hard disk systems.
Chung, Tony; Truant, Daniel; Morriss, Gary P
2010-06-01
We demonstrate the preservation of the Lyapunov modes in a system of hard disks by the underlying tangent space dynamics. This result is exact for the Zero modes and correct to order ϵ for the Transverse and Longitudinal-Momentum modes, where ϵ is linear in the mode number. For sufficiently large mode numbers, the ϵ terms become significant and the dynamics no longer preserves the mode structure. We propose a modified Gram-Schmidt procedure based on orthogonality with respect to the center zero space that produces the exact numerical mode. This Gram-Schmidt procedure can also exploit the orthogonality between conjugate modes and their symplectic structure in order to find a simple relation that determines the Lyapunov exponent from the Lyapunov mode. This involves a reclassification of the modes into either direction preserving or form preserving. These analytic methods assume a knowledge of the ordering of the modes within the Lyapunov spectrum, but gives both predictive power for the values of the exponents from the modes and describes the modes in greater detail than was previously achievable. Thus the modes and the exponents contain the same information.
Qualitative and quantitative stability analysis of penta-rhythmic circuits
Schwabedal, Justus T. C.; Knapper, Drake E.; Shilnikov, Andrey L.
2016-12-01
Inhibitory circuits of relaxation oscillators are often-used models for dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three generic oscillators (of a Fitzhugh-Nagumo type) as its nodes coupled reciprocally. Depending on inhibitory strengths, and parameters of individual oscillators, the circuit exhibits polyrhythmicity of up to five simultaneously stable rhythms. With methods of bifurcation analysis and phase reduction, we investigate qualitative changes in stability of these circuit rhythms for a wide range of parameters. Furthermore, we quantify robustness of the rhythms maintained under random perturbations by monitoring phase diffusion in the circuit. Our findings allow us to describe how circuit dynamics relate to dynamics of individual nodes. We also find that quantitative and qualitative stability properties of polyrhythmicity do not always align.
An Efficient and Configurable Preprocessing Algorithm to Improve Stability Analysis.
Sesia, Ilaria; Cantoni, Elena; Cernigliaro, Alice; Signorile, Giovanna; Fantino, Gianluca; Tavella, Patrizia
2016-04-01
The Allan variance (AVAR) is widely used to measure the stability of experimental time series. Specifically, AVAR is commonly used in space applications such as monitoring the clocks of the global navigation satellite systems (GNSSs). In these applications, the experimental data present some peculiar aspects which are not generally encountered when the measurements are carried out in a laboratory. Space clocks' data can in fact present outliers, jumps, and missing values, which corrupt the clock characterization. Therefore, an efficient preprocessing is fundamental to ensure a proper data analysis and improve the stability estimation performed with the AVAR or other similar variances. In this work, we propose a preprocessing algorithm and its implementation in a robust software code (in MATLAB language) able to deal with time series of experimental data affected by nonstationarities and missing data; our method is properly detecting and removing anomalous behaviors, hence making the subsequent stability analysis more reliable.
A Method for stability analysis of magnetic bearings : Basic stability criteria
Shayak, B
2016-01-01
In this work I outline a general procedure for dynamic modeling and stability analysis of a magnetic bearing, which is a rotating shaft confined inside a chamber through electromagnetic forces alone. I consider the simplest type of self-propelled bearing, namely a permanent magnet synchronous motor and an induction motor rotor freely suspended inside the corresponding stator, and having no eccentricity-fedback control algorithm. Writing Euler's equations for the rotor mechanics and Maxwell's equations for the electromagnetic field leads to a systematic technique for analysing the dynamics of the complete system. Physical arguments indicate that that two essential components for rotor confinement are a spatial gradient in the stator magnetic field and a torque angle lying in the second quadrant. These predictions are confirmed through the linear stability analysis. The direct practical utility of the results is mitigated by the presence of a repeated eigenvalue in the linearized equations. Despite this limitat...
Stability Analysis for Compliant Constant-Force Compression Mechanisms
Directory of Open Access Journals (Sweden)
Ikechukwu Celestine UGWUOKE
2009-12-01
Full Text Available Stability analysis in compliant mechanism (CM design is of utmostimportance. From a practical point of view, a CM that is unstable is of nosignificance (has no practical value. Three useful plots were considered in theevaluation of each of the dynamic models of nine configurations of compliantconstant-force compression mechanisms (CCFCMs for their stabilitycharacteristics, which includes the polar plot based on the Routh-Hurwitzstability criterion, the Bode plot, and the Nyquist diagram which considersstability in the real frequency domain. Frequency-domain stability criterion isvery useful for determining suitable approaches to adjusting the CCFCMparameters in order to increase its relative stability. The results obtained showthat the CCFCMs investigated do exhibit higher relative stability for highervalues of damping ratio, and for zero damping ratio, all the CCFCMsinvestigated were unstable. The result also show that for the CCFCMsinvestigated to be stable, damping ratio must be greater than 0.03 (ξ > 0.03and depending on what attributes are most desirable, the CCFCM parameterscan be optimized to achieve the desired results. Nyquist criterion provides uswith suitable information concerning the absolute stability and furthermore,can be utilized to define and ascertain the relative stability of a system.
Lyapunov matrices approach to the parametric optimization of time-delay systems
Directory of Open Access Journals (Sweden)
Duda Józef
2015-09-01
Full Text Available In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix
Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays
Directory of Open Access Journals (Sweden)
Duda Jozef
2016-09-01
Full Text Available In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the Lyapunov functional for the initial function of time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. A...
A tutorial on incremental stability analysis using contraction theory
DEFF Research Database (Denmark)
Jouffroy, Jerome; Fossen, Thor I.
2010-01-01
This paper introduces a methodology for dierential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct steps: the descriptions of two systems to be compared (the plant and the observer in the case of observer convergence anal...
Transient stability analysis of a distribution network with distributed generators
Xyngi, I.; Ishchenko, A.; Popov, M.; Van der Sluis, L.
2009-01-01
This letter describes the transient stability analysis of a 10-kV distribution network with wind generators, microturbines, and CHP plants. The network being modeled in Matlab/Simulink takes into account detailed dynamic models of the generators. Fault simulations at various locations are investigat
Bank stability analysis for fluvial erosion and mass failure
The central objective of this study was to highlight the differences in magnitude between mechanical and fluvial streambank erosional strength with the purpose of developing a more comprehensive bank stability analysis. Mechanical erosion and ultimately failure signifies the general movement or coll...
Delay-slope-dependent stability results of recurrent neural networks.
Li, Tao; Zheng, Wei Xing; Lin, Chong
2011-12-01
By using the fact that the neuron activation functions are sector bounded and nondecreasing, this brief presents a new method, named the delay-slope-dependent method, for stability analysis of a class of recurrent neural networks with time-varying delays. This method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed Lyapunov-Krasovskii functional. Then some improved delay-dependent stability criteria with less computational burden and conservatism are obtained. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.
Stability and Control of Large-Scale Dynamical Systems A Vector Dissipative Systems Approach
Haddad, Wassim M
2011-01-01
Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynami
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
Stability analysis of cosmological models through Liapunov's method
Charters, T C; Mimoso, J P; Charters, Tiago C.; Mimoso, Jose P.
2001-01-01
We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first order perturbation techniques. Moreover, Liapunov's method is also applicable to non-autonomous systems. We use this advantadge to investigate the mechanism of reheating for the inflaton field in FRW models.
Stability analysis of a buck regulator employing input filter compensation
Kelkar, S. S.; Lee, F. C.
1983-01-01
The interaction between the input filter and the regulator often causes serious degradation of performance. The reduction in loop gain due to input filter interaction can result in system instability. An exact stability analysis of the buck regulator system is presented. The input filter parameter values are varied and system instability is predicted for the case without feedforward. The eigenvalues of the system can be brought back into the unit circle and the system thus stabilized with the addition of the feedforward loop. Measurements made for the cases with and without feedforward confirm the analytical prediction.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Stability analysis of underground openings for extraction of natural stone
Directory of Open Access Journals (Sweden)
Karmen Fifer Bizjak
2003-06-01
Full Text Available Extraction of natural stone is usually carried out in surface quarries. Underground excavation is not a frequently used method. Due to the restrictive environmental legislature and limited stores of natural stone, underground extraction has become quite an interestingalternative. Dimensions of underground openings are determined with stability analyses.Prior to starting a numerical analysis of a large underground opening it is very important to determine the mechanism of failure and set up a proper numerical model. The continuum method is usually used in rock mechanics. A disadvantage of this calculation is that it cannotbe applied to a large number of joints. Other methods are preferred, such as the numerical discrete method, which allows joint systems to be involved into calculations. The most probable failure of rock with several joint systems is block sliding. In the example of themarble of Hotavlje both methods were used. It was established that the continuum method is convenient for the global stability prediction of the underground opening. Further discretemethod enable the block stability calculation. The analytical block analysis is still accurate for the a stability calculation of single block. The prerequisite for a good numerical analysis is sufficient quality data on geomechanical properties of rock. In-situ tests, laboratory tests and geotechnical measurements on the site are therefore necessary. Optimum dimensions of underground chambers in the Quarry of Hotavlje were calculated by using several numericalmodels, and the maximum chamber width of 12 m was obtained.
QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Hui-ping; XUE Yu-sheng; CHEN Yu-shu
2005-01-01
Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quanttative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal beatings with nonlinear suspensionare are determined.
Lyapunov exponent for aging process in induction motor
Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat
2012-09-01
Nonlinear systems like electrical circuits and systems, mechanics, optics and even incidents in nature may pass through various bifurcations and steady states like equilibrium point, periodic, quasi-periodic, chaotic states. Although chaotic phenomena are widely observed in physical systems, it can not be predicted because of the nature of the system. On the other hand, it is known that, chaos is strictly dependent on initial conditions of the system [1-3]. There are several methods in order to define the chaos. Phase portraits, Poincaré maps, Lyapunov Exponents are the most common techniques. Lyapunov Exponents are the theoretical indicator of the chaos, named after the Russian mathematician Aleksandr Lyapunov (1857-1918). Lyapunov Exponents stand for the average exponential divergence or convergence of nearby system states, meaning estimating the quantitive measure of the chaotic attractor. Negative numbers of the exponents stand for a stable system whereas zero stands for quasi-periodic systems. On the other hand, at least if one of the exponents is positive, this situation is an indicator of the chaos. For estimating the exponents, the system should be modeled by differential equation but even in that case mathematical calculation of Lyapunov Exponents are not very practical and evaluation of these values requires a long signal duration [4-7]. For experimental data sets, it is not always possible to acquire the differential equations. There are several different methods in literature for determining the Lyapunov Exponents of the system [4, 5]. Induction motors are the most important tools for many industrial processes because they are cheap, robust, efficient and reliable. In order to have healthy processes in industrial applications, the conditions of the machines should be monitored and the different working conditions should be addressed correctly. To the best of our knowledge, researches related to Lyapunov exponents and electrical motors are mostly
THE FINANCIAL STABILITY ANALYSIS THROUGH THE WORKING CAPITAL
Directory of Open Access Journals (Sweden)
LĂPĂDUŞI MIHAELA LOREDANA
2012-12-01
Full Text Available The main goal of any business is to maintain the financial stability not only on the short term but also on medium and long term, in other words to maintain a harmony between financial sources and financial needs, respectively the equality between the assets and liabilities from the balance sheet. On short term, maintaining the financial stability involves correlating the temporary resources with the temporary uses by using the necessary working capital, and on the long-term, the financial stability involves comparing the permanent resources with the permanent uses by working capital indicator. The determination of the financial state of the company at a certain moment represents the key moment in establishing and adopting the economic and financial decisions in the management of the company. Maintaining the financial stability of the company represents one of the main objectives of the financial analysis and management and it also provides the optimum development of the entire economic and financial activity of the company. The analysis of the working capital size is based on the financial statement data and information, and based on this analysis is considered the financial situation of the company, the financial equilibrium state at a certain moment. The purpose of this article is to highlight the fact that the maintenance of the financial stability on medium and long term is subordinated to the “working capital” indicator, its content and interpretation evolving in time and varying differently from one company to another. The results of this research may have broad applicability in the field of the companies’ activity and it materializes in the complex approach of the working capital regarded as a classic indicator, frequently used in the financial analysis and with profound significance in establishing the financial state in general and the equilibrium state in particular.
Constitutive models in stability analysis of rock slope
Institute of Scientific and Technical Information of China (English)
言志信; 段建; 王后裕
2008-01-01
Equivalent Mohr-Coulomb yield criterion was established,and the relationship between different constitutive models was studied.The application of equivalent Mohr-Coulomb yield criterion in Ansys was achieved by means of transforming material parameters.The stability research aiming at the most common rock slope without conspicuous slide surface was accomplished,the methods of measurably assessing the stability of rock slope without conspicuous slide surface were explored,and the disadvantages of method of minimum slide-resisted reserve as dangerous slide path were pointed out.The results show that through the calculation and analysis of cases,the conception that measurable assessment of the stability of rock slope without conspicuous slide surface can be achieved under condition that equivalent Mohr-Coulomb yield criterion is validated.Its safety parameter formula is explicit in theory and credible in results.The results obtained are approximate to those obtained by using finite element intensity reducing method.
Stability and Sensitivity Analysis of Fuzzy Control Systems. Mechatronics Applications
Directory of Open Access Journals (Sweden)
Radu-Emil Precup
2006-01-01
Full Text Available The development of fuzzy control systems is usually performed by heuristicmeans, incorporating human skills, the drawback being in the lack of general-purposedevelopment methods. A major problem, which follows from this development, is theanalysis of the structural properties of the control system, such as stability, controllabilityand robustness. Here comes the first goal of the paper, to present a stability analysismethod dedicated to fuzzy control systems with mechatronics applications based on the useof Popov’s hyperstability theory. The second goal of this paper is to perform the sensitivityanalysis of fuzzy control systems with respect to the parametric variations of the controlledplant for a class of servo-systems used in mechatronics applications based on theconstruction of sensitivity models. The stability and sensitivity analysis methods provideuseful information to the development of fuzzy control systems. The case studies concerningfuzzy controlled servo-systems, accompanied by digital simulation results and real-timeexperimental results, validate the presented methods.
A delay-range-partition approach to analyse stability of linear systems with time-varying delays
Xue, Y.; Zhang, X.; Han, Y. Y.; Shi, M.
2016-12-01
In this paper, the stability analysis of linear systems with an interval time-varying delay is investigated. First, augmented Lyapunov-Krasovskii functionals are constructed, which include more information of the delay's range and the delay's derivative. Second, two improved integral inequalities, which are less conservative than Jensen's integral inequalities, and delay-range-partition approach are utilised to estimate the upper bounds of the derivatives of the augmented Lyapunov-Krasovskii functionals. Then, less conservative stability criteria are proposed no matter whether the lower bound of delay is zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numerical examples are given and their results are compared with the existing results.
A New Approach for Aeroelastic Robust Stability Analysis
Institute of Scientific and Technical Information of China (English)
Wu Zhigang; Yang Chao
2008-01-01
Air vehicles undergo variations in structural mass and stiffness because of fuel consumption and the failure of structural components, which might lead to serious influences on the aeroelastic characteristics. An approach for aeroelastic robust stability analysis taking into account the perturbations of structural mass and stiffness is developed. Applying the perturbation method and harmonic unsteady aerodynamic forces, the frequency-domain linear fractal transformation (LFT) representation of pertorbed aeroelastic system is modeled.Then, the robust stability is analyzed by using the structured singular value μ-method. The numerical results of a bi-spar wing show its effectiveness and low computational time in dealing with the robust problems with mass and stiffness perturbations. In engineering analysis for solving aeroelastic problems, the robust approach can be applied to flutter analysis for airplane with the fuel load variation and taking the damage conditions into consideration.
Global analysis on slope stability and its engineering application
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In hydraulic engineering, sometimes it is necessary to consider the stability of sliding bodies with lateral frictional boundaries. Neither the existing three dimensional limit equilibrium methods nor the commercial software products are able to treat such situations. The three dimensional factor of safety is accordingly underestimated; while the shearing strength based on the three dimensional back analysis is overestimated. In this study, the lateral boundaries are regarded as the part of the slip surface. Based on the expression of the normal pressure on the slip surface and the patch interpolation, a rigorous solution for the three dimensional limit equilibrium analysis is realized. Meanwhile, the proposed procedure is applied to the stability analysis of the slope with a cable platform on the right bank in Da Gang Shan hydraulic project under construction.
Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles
2011-06-01
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
Analysis and Control of the Pan System via Sliding Mode Control
Sundarapandian Vaidyanathan
2012-01-01
In this paper, we obtain new results for the analysis and control of the Pan system (2010) using sliding mode control (SMC). The stability results derived in this paper for the control of the Pan system to stabilize about its unstable equilibrium at the origin have been derived using sliding mode control and Lyapunov stability theory. Numerical simulations are depicted to demonstrate the control results derived in this paper.
Stability of the Newton-Like algorithm in optimization flow control
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The stability of the Newton-like algorithm in optimization flow control is considered in this paper.This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theory, without considering the round trip time of each source. While the stability of this algorithm with considering the round trip time is analyzed as well. The analysis shows that the algorithm with only one bottleneck link accessed by several sources is also globally stable, and all trajectories described by this algorithm ultimately converge to the equilibrium point.
An, Jiyao; Li, Zhiyong; Wang, Xiaomei
2014-03-01
This paper considers the problem of delay-fractional-dependent stability analysis of linear systems with interval time-varying state delay. By developing a delay variable decomposition approach, both the information of the variable dividing subinterval delay, and the information of the lower and upper bound of delay can be taken into full consideration. Then a new delay-fractional-dependent stability criterion is derived without involving any direct approximation in the time-derivative of the Lyapunov-Krasovskii (LK) functional via some suitable Jensen integral inequalities and convex combination technique. The merits of the proposed result lie in less conservatism, which are realized by choosing different Lyapunov matrices in the variable delay subintervals and estimating the upper bound of some cross term in LK functional more exactly. At last, two well-known numerical examples are employed to show the effectiveness and less conservatism of the proposed method.
Stochastic stability of mechanical systems under renewal jump process parametric excitation
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R.K.; Larsen, Jesper Winther
2005-01-01
if the state space is augmented by the products of the original state variables and the excitation variable. Asymptotic mean and mean-square stability as well as asymptotic sample (Lyapunov) stability with probability 1 are investigated. The Lyapunov exponents have been evaluated both by the direct simulation...
STABILITY OF SOLUTIONS TO CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.