dependent time-delay: Stability and stabilizability
Directory of Open Access Journals (Sweden)
E. K. Boukas
2002-01-01
Full Text Available This paper considers stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of systems. A control design algorithm is also provided. A numerical example is given to demonstrate the effectiveness of the obtained theoretical results.
On delay-dependent robust stability of neutral systems
Institute of Scientific and Technical Information of China (English)
Renxin ZHONG; Zhi YANG; Guoli WANG
2006-01-01
The delay-dependent robust stability of uncertain linear neutral systems with delays is investigated. Both discrete-delay-dependent/neutral-delay-independent and neutral-/discrete- delay-dependent stability criteria will be developed. The proposed stability criteria are formulated in the form of linear matrix inequalities and it is easy to check the robust stability of the considered systems. By introducing certain Lyapunov-Krasovskii functional the mathematical development of our result avoids model transformation and bounding for cross terms, which lead to conservatism. Finally, numerical example is given to indicate the improvement over some existing results.
Institute of Scientific and Technical Information of China (English)
Huaicheng YAN; Xinhan HUANG; Min WANG
2006-01-01
This paper deals with the problem of delay-dependent stability and stabilization for networked control systems(NCSs)with multiple time-delays. In view of multi-input and multi-output(MIMO) NCSs with many independent sensors and actuators, a continuous time model with distributed time-delays is proposed. Utilizing the Lyapunov stability theory combined with linear matrix inequalities(LMIs) techniques, some new delay-dependent stability criteria for NCSs in terms of generalized Lyapunov matrix equation and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs. Compared with the reported methods, the proposed methods give a less conservative delay bound and more general results. Numerical example and simulation show that the methods are less conservative and more effective.
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).
Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems
Institute of Scientific and Technical Information of China (English)
Gao Huanli; Xu Bugong
2008-01-01
The problem of robust stabilization for uncertain singular time-delay systems is studied.First,a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given,which is less conservative.Using this result,the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed.Finally,two examples are given to illustrate the effectiveness of the results.
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.
Delay-Dependent Exponential Stability Criterion for BAM Neural Networks with Time-Varying Delays
Institute of Scientific and Technical Information of China (English)
Wei-Wei Su; Yi-Ming Chen
2008-01-01
By employing the Lyapunov stability theory and linear matrix inequality (LMI) technique, delay dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory (BAM) neural networks with time-varying delays. The proposed condition can be checked easily by LMI control toolbox in Matlab. A numerical example is given to demonstrate the effectiveness of our results.
Improving Delay-Range-Dependent Stability Condition for Systems with Interval Time-Varying Delay
Directory of Open Access Journals (Sweden)
Wei Qian
2013-01-01
Full Text Available This paper discusses the delay-range-dependent stability for systems with interval time-varying delay. Through defining the new Lyapunov-Krasovskii functional and estimating the derivative of the LKF by introducing new vectors, using free matrices and reciprocally convex approach, the new delay-range-dependent stability conditions are obtained. Two well-known examples are given to illustrate the less conservatism of the proposed theoretical results.
On delay-dependent robust stability for uncertain neutral systems
Institute of Scientific and Technical Information of China (English)
He Yong; Wu Min
2005-01-01
The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-eal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some freeweighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.
Delay-dependent criteria for the robust stability of systems with time-varying delay
Institute of Scientific and Technical Information of China (English)
Min WU; Yong HE; Jinhua SHE
2003-01-01
The problem of delay-dependent robust stability for systems with titne-varying delay has been considered. By using the S-procedure and the Park' s inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.
Institute of Scientific and Technical Information of China (English)
Dejin WANG
2003-01-01
This article concerns a coupled LMIs approach to delay-dependent observer-based output feedback stabilizing controller design for linear continuous-time systems with multiple state delays. The advantage of our proposed delay-dependent coupled LMIs criterion lies in that: (1) it can optimize one of multiple time delays with others selected properly, and at the same time, the feedback-gain and observer-gain can be obtained, respectively. (2) it is less conservative than the existing delay-independent ones in the literature. Algorithm to solve the coupled LMIs is also given. Numerical examples illustrate the effectiveness of our method.
Institute of Scientific and Technical Information of China (English)
Huaicheng YAN; Xinhan HUANG; Min WANG
2007-01-01
In this paper, delay-dependent robust stability for a class of uncertain networked control systems (NCSs)with multiple state time-delays is investigated. Modeling of multi-input and multi-output (MIMO) NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound (MADB) for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.
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.
A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Niu Yuanling; Zhang Chengjian; Duan Jinqiao
2011-01-01
A type of complex systems under both random influence and memory effects is considered.The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations.A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough.Numerical simulations are presented to illustrate the theoretical result.
Institute of Scientific and Technical Information of China (English)
Zhengguang WU; Wuneng ZHOU
2008-01-01
This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality(LMI)approach.Based on a delay-dependent stability condition for the nominal system,a state feedback controller is designed,which guarantees the resultant closedloop system to be robustly stable.An explicit expression for the desired controller is also given by solving a set of matrix inequalities.Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.
Delay dependent stability criteria for recurrent neural networks with time varying delays
Institute of Scientific and Technical Information of China (English)
Zhanshan WANG; Huaguang ZHANG
2009-01-01
This paper aims to present some delay-dependent global asymptotic stability criteria for recurrent neural networks with time varying delays.The obtained results have no restriction on the magnitude of derivative of time varying delay,and can be easily checked due to the form of linear matrix inequality.By comparison with some previous results,the obtained results are less conservative.A numerical example is utilized to demonstrate the effectiveness of the obtained results.
Mixed delay-independent/delay-dependent stability of uncertain linear time-delayed systems
Institute of Scientific and Technical Information of China (English)
LI Wenlin; DONG Rui
2004-01-01
@@ Consider uncertain linear time delay systems described by the following state equation: x(t)=[A0+Δ A0(t)]x(t)+∑ri=1[Ai+ΔAi(t)]x(t-τi).(1) x(t)=(t)t∈[-,0];=maxri=1{τi}(2) where Δ A0(*) and Δ Ai(*)(i=1,…,r) are real matrix functions.Δ Ai(t)=LiFi(t)Ei,ΔA0(t)=L0F0(t)E0, where Li,Ei are known real constant matrices and Fi(t) are unknown real time-varying matrices with Lebesgue measurable elements satisfying ‖Fi(t)‖I,t(i=0,1,…,r). In this note, we develop the methods of robust stability which is dependent on the size of some delays but independent on the size of the others and is based on the solution of linear matrix inequalities.
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.
Delay-dependent stability analysis for discrete-time systems with time varying state delay
Directory of Open Access Journals (Sweden)
Stojanović Sreten B.
2011-01-01
Full Text Available The stability of discrete systems with time-varying delay is considered. Some sufficient delaydependent stability conditions are derived using an appropriate model transformation of the original system. The criteria are presented in the form of LMI, which are dependent on the minimum and maximum delay bounds. It is shown that the stability criteria are approximately the same conservative as the existing ones, but have much simpler mathematical form. The numerical example is presented to illustrate the applicability of the developed results.
Delay-dependent stabilization of singular Markovian jump systems with state delay
Institute of Scientific and Technical Information of China (English)
Zhengguang WU; Hongye SU; Jian CHU
2009-01-01
This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays.A delay-dependent condition is established for the considered system to be regular,impulse free and stochastically stable.Based on the condition,a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular,impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities (LMIs).Numerical examples show the effectiveness of the proposed methods.
Delay-Dependent Asymptotic Stability of Cohen-Grossberg Models with Multiple Time-Varying Delays
Directory of Open Access Journals (Sweden)
Xiaofeng Liao
2007-01-01
Full Text Available Dynamical behavior of a class of Cohen-Grossberg models with multiple time-varying delays is studied in detail. Sufficient delay-dependent criteria to ensure local and global asymptotic stabilities of the equilibrium of this network are derived by constructing suitable Lyapunov functionals. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
Delay-dependent robust stability for neutral systems with mixed discrete-and-neutral delays
Institute of Scientific and Technical Information of China (English)
Yong HE; Min WU; Jinhua SHE
2004-01-01
This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and-neutral delays and time-varying structured uncertainties.Some new criteria are presented,in which some free weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula.The criteria include the information on the size of both neutral-and-discrete delays.It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases.A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.
Further triple integral approach to mixed-delay-dependent stability of time-delay neutral systems.
Wang, Ting; Li, Tao; Zhang, Guobao; Fei, Shumin
2017-09-01
This paper studies the asymptotic stability for a class of neutral systems with mixed time-varying delays. Through utilizing some Wirtinger-based integral inequalities and extending the convex combination technique, the upper bound on derivative of Lyapunov-Krasovskii (L-K) functional can be estimated more tightly and three mixed-delay-dependent criteria are proposed in terms of linear matrix inequalities (LMIs), in which the nonlinearity and parameter uncertainties are also involved, respectively. Different from those existent works, based on the interconnected relationship between neutral delay and state one, some novel triple integral functional terms are constructed and the conservatism can be effectively reduced. Finally, two numerical examples are given to show the benefits of the proposed criteria. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
A Stability Condition with Delay-Dependence 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 By using the time-switched method and the comparison theorem, we derived a criterion of delay-dependent stability for the switched large-scale time-delay systems. To guarantee the exponential stability for the switched large-scale time-delay systems with stability margin λ, the total activation time ratio of the switching law is determined. An example is used to illustrate the effectiveness of our result.
Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays
Directory of Open Access Journals (Sweden)
Yonggang Chen
2008-01-01
Full Text Available This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI. Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.
New Delay-Dependent Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delays
Institute of Scientific and Technical Information of China (English)
Liang Lin XIONG; Shou Ming ZHONG; Mao YE
2011-01-01
This paper deals with the issues of robust stability for uncertain discrete-time switched systems with mode-dependent time delays. Based on a novel difference inequality and a switched Lyapunov function, new delay-dependent stability criteria are formulated in terms of linear matrix inequalities (LMIs) which are not contained in known literature. A numerical example is given to demonstrate that the proposed criteria improves some existing results significantly with much less computational effort.
Delay-dependent asymptotic stability for neural networks with time-varying delays
Directory of Open Access Journals (Sweden)
Xiaofeng Liao
2006-01-01
ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
Delay-Dependent Absolute Stability ofUncertain Lur′e Systems with Time-Delays1）
Institute of Scientific and Technical Information of China (English)
CHENWu-Hua; GUANZhi-Hong; LUXiao-Mei; YANGXuan-Fang
2004-01-01
This paper is concerned with delay dependent absolute stability for a class of uncertain Lur′e systems with multiple time-delays. By using a descriptor model transformation of the sys-tem and by applying a recent result on bounding of cross products of vectors, a new type of Lya-punov-Krasovskii functional is constructed. Based on the new functional, delay-dependent suffi-cient conditions for absolute stability are derived in terms of linear matrix inequalities. These con-ditions do not require any parameter tuning, and can be solved numerically using the software LMI Lab. A numerical example is presented which shows that the proposed method can substantiallyimprove the delay bound for absolute stability of Lur′e system with time-delays, compared to theexisting ones.
Directory of Open Access Journals (Sweden)
Weihua Mao
2012-01-01
Full Text Available This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs. By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Hamid Reza Karimi
2009-01-01
Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.
Delay-dependent asymptotic stability of mobile ad-hoc networks: A descriptor system approach
Yang, Juan; Yang, Dan; Huang, Bin; Zhang, Xiao-Hong; Luo, Jian-Lu
2014-07-01
In order to analyze the capacity stability of the time-varying-propagation and delay-dependent of mobile ad-hoc networks (MANETs), in this paper, a novel approach is proposed to explore the capacity asymptotic stability for the delay-dependent of MANETs based on non-cooperative game theory, where the delay-dependent conditions are explicitly taken into consideration. This approach is based on the Lyapunov—Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique. A corresponding Lyapunov—Krasovskii functional is introduced for the stability analysis of this system with use of the descriptor and “neutral-type” model transformation without producing any additional dynamics. The delay-dependent stability criteria are derived for this system. Conditions are given in terms of linear matrix inequalities, and for the first time referred to neutral systems with the time-varying propagation and delay-dependent stability for capacity analysis of MANETs. The proposed criteria are less conservative since they are based on an equivalent model transformation. Furthermore, we also provide an effective and efficient iterative algorithm to solve the constrained stability control model. Simulation experiments have verified the effectiveness and efficiency of our algorithm.
Institute of Scientific and Technical Information of China (English)
LIU Hai-feng; WANG Chun-hua; WEI Guo-liang
2008-01-01
The exponential stability problem is investigated fora class of stochastic recurrent neural networks with time delay and Markovian switching.By using It(o)'s differential formula and the Lyapunov stabifity theory,sufficient condition for the solvability of this problem is derived in telm of linear matrix inequalities,which can be easily checked by resorting to available software packages.A numerical example and the simulation are exploited to demonstrate the effectiveness of the proposed results.
Delay-dependent H2 control for discrete time-delay systems with D-stability constraints
Institute of Scientific and Technical Information of China (English)
Man Sun; Yingmin Jia; Junping Du; Shiying Yuan
2008-01-01
This paper studies the problem of H2 control for a class of discrete time-delay systems with D-stability constraints. The corresponding sufficient conditions are given in terms of linear matrix inequalities. In particular, the conditions are delay-dependent, and so they are less conservative. The obtained controller can provide an upper bound for the H2 cost function. A numerical example is given to illustrate the proposed method.
Liu, Pin-Lin
2013-11-01
This paper provides an improved delay-range-dependent stability criterion for linear systems with interval time-varying delays. No model transformation and no slack matrix variable are introduced. Furthermore, overly bounding for some cross term is avoided. The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Finally, two numerical examples are given to show the effectiveness of the proposed results.
Directory of Open Access Journals (Sweden)
Xing Yin
2011-01-01
uncertain periodic switched recurrent neural networks with time-varying delays. When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach (SQLF and free-weighting matrix approach (FWM, some linear matrix inequality criteria are found to guarantee the delay-dependent asymptotical stability of these systems. Two examples illustrate the exactness of the proposed criteria.
Institute of Scientific and Technical Information of China (English)
Renji Han; Wei Jiang
2009-01-01
The problem of delay-dependent robust stability for uncertain linear singular neu-tral systems with time-varying and distributed delays is investigated. The uncertain-ties under consideration are norm bounded, and possibly time varying. Some new stability criteria, which are simpler and less conservative than existing results, are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coefficient matrix and formulated in the form of a linear matrix inequalitys (LMIs). Also, the criteria can be easily checked by the Matlab LMI toolbox.
Institute of Scientific and Technical Information of China (English)
Wang Shen-Quan; Feng Jian; Zhao Qing
2012-01-01
In this paper,the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks (CRNNs) with stochastic delay.Different from the common assumptions on time delays,it is assumed that the probability distribution of the delay taking values in some intervals is known a priori.By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique (the reciprocally convex combination method),less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities (LMIs).Two numerical examples show that our results are better than the existing ones.
Yan, Zhiguo; Song, Yunxia; Park, Ju H
2017-05-01
This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
PERSISTENCE AND STABILITY IN A RATIO-DEPENDENT FOOD-CHAIN SYSTEM WITH TIME DELAYS
Institute of Scientific and Technical Information of China (English)
XuRui; FengHanying; YangPinghua; WangZhiqiang
2002-01-01
A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.
Stability and Bifurcation in a State-Dependent Delayed Predator-Prey System
Hou, Aiyu; Guo, Shangjiang
In this paper, we consider a class of predator-prey equations with state-dependent delayed feedback. Firstly, we investigate the local stability of the positive equilibrium and the existence of the Hopf bifurcation. Then we use perturbation methods to determine the sub/supercriticality of Hopf bifurcation and hence the stability of Hopf bifurcating periodic solutions. Finally, numerical simulations supporting our theoretical results are also provided.
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.
Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system
Institute of Scientific and Technical Information of China (English)
Wan-Yong Wang; Li-Jun Pei
2011-01-01
Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria,and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluctuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover
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.
Liu, Qun
2015-02-01
In this paper, a stochastic Lotka-Volterra competitive model with time-dependent delays is investigated. Sufficient conditions for global asymptotic stability of the positive equilibrium are established. The obtained result demonstrates that time-dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system.
Xinghua Liu; Hongsheng Xi
2013-01-01
The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciproca...
Kao, Yonggui; Wang, Changhong; Xie, Jing; Karimi, Hamid Reza
2016-08-01
This paper investigates the delay-dependent stability problem for neutral Markovian jump systems with generally unknown transition rates (GUTRs). In this neutral GUTR model, each transition rate is completely unknown or only its estimate value is known. Based on the study of expectations of the stochastic cross-terms containing the ? integral, a new stability criterion is derived in terms of linear matrix inequalities. In the mathematical derivation process, bounding stochastic cross-terms, model transformation and free-weighting matrix are not employed for less conservatism. Finally, an example is provided to demonstrate the effectiveness of the proposed results.
Zheng, Cheng-De; Shan, Qi-He; Zhang, Huaguang; Wang, Zhanshan
2013-05-01
The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization 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.
New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay
Institute of Scientific and Technical Information of China (English)
ZHANG HuaGuang; WANG ZhanShan
2009-01-01
This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results.
Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations.A new stabilization/stability scheme is presented.Using improved Lyapunov functionals.less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities(LMI).Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.
Louihi, M.; Hbid, M. L.
2007-05-01
In this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays. Our approach is based on the Crandall-Liggett approximation and the properties of semigroups.
Directory of Open Access Journals (Sweden)
Kaibo Shi
2014-01-01
Full Text Available This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.
Directory of Open Access Journals (Sweden)
Sirada Pinjai
2013-01-01
Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness 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.
Delay-independent stabilization for teleoperation with time varying delay
Fujita, Hiroyuki; Namerikawa, Toru
2009-01-01
This paper deals with the stability for nonlinear teleoperation with time varying communication delays. The proposed method is passivity-based controllers with time varying gains which depend on the rate of change of time varying delay. In our proposed method, stability condition is independent of the magnitude of the communication delay and the damping of the system. The delay-independent stability is shown via Lyapunov stability methods. Several experimental results show the effectiveness o...
Zhang, Guodong; Shen, Yi
2015-11-01
This paper is concerned with the global exponential stability on a class of delayed neural networks with state-dependent switching. Under the novel conditions, some sufficient criteria ensuring exponential stability of the proposed system are obtained. In particular, the obtained conditions complement and improve earlier publications on conventional neural networks with continuous or discontinuous right-hand side. Numerical simulations are also presented to illustrate the effectiveness of the obtained results.
Global stability for delay-dependent HTLV-I model with CTL immune response
Wang, Yan; Liu, Jun
2016-06-01
We present a delay-dependent HTLV-I model with CTL immune response. The basic reproduction number is obtained for the existence of positive steady state. By constructing suitable Lyapunov functions, when the basic reproduction number is less than one, the infection-free steady state is globally asymptotically stable; when the basic reproduction number is greater than one, the infected steady state is globally asymptotically stable.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.
Stability and delay sensitivity of neutral fractional-delay systems
Xu, Qi; Shi, Min; Wang, Zaihua
2016-08-01
This paper generalizes the stability test method via integral estimation for integer-order neutral time-delay systems to neutral fractional-delay systems. The key step in stability test is the calculation of the number of unstable characteristic roots that is described by a definite integral over an interval from zero to a sufficient large upper limit. Algorithms for correctly estimating the upper limits of the integral are given in two concise ways, parameter dependent or independent. A special feature of the proposed method is that it judges the stability of fractional-delay systems simply by using rough integral estimation. Meanwhile, the paper shows that for some neutral fractional-delay systems, the stability is extremely sensitive to the change of time delays. Examples are given for demonstrating the proposed method as well as the delay sensitivity.
Institute of Scientific and Technical Information of China (English)
何勇; 吴敏
2005-01-01
Some delay-dependent absolute stability criteria for Lurie control systems with timevarying delay are derived, in which some free-weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI. Moreover, the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems. Finally, some examples axe provided to demonstrate the effectiveness of the proposed methods.
Institute of Scientific and Technical Information of China (English)
吴争光; 周武能
2007-01-01
This paper considers the problem of delay-dependent robust stabilization for uncertain singular delay systems. In terms of linear matrix inequality (LMI) approach, a delay-dependent stability criterion is given to ensure that the nominal system is regular, impulse free, and stable. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. An explicit expression for the desired controller is also given. Some numerical examples are provided to illustrate the validity of the proposed methods.
Institute of Scientific and Technical Information of China (English)
杜昭平; 张庆灵; 刘丽丽
2009-01-01
In this paper, the problem of delay-dependent robust stabilization is investigated for singular systems with multiple input delays and admissible uncertainties. First, an improved delay-dependent stabilization criterion for the nominal system is established in terms of linear matrix inequalities (LMIs). Then, based on this criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. Numerical examples are provided to illustrate the effectiveness of the proposed method.
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.
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.
Institute of Scientific and Technical Information of China (English)
吴敏; 何勇; 佘锦华
2005-01-01
This paper concerns problem of the delay-dependent robust stability and stabilization for uncertain neutral systems. Some new delay-dependent stability criteria are derived by taking matrices are given to express the relationship between the terms in the Leibniz-Newton formula and the new criteria are based on linear matrix inequalities such that the free weighting matrices can be easily obtained. Moreover, the stability criteria are also used to design the state-feedback controller.Numerical examples demonstrates that the proposed criteria are effective and are an improvement over the previous papers.
Institute of Scientific and Technical Information of China (English)
徐瑞; 陈兰荪
2002-01-01
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.
Basin stability in delayed dynamics
Leng, Siyang; Lin, Wei; Kurths, Jürgen
2016-02-01
Basin stability (BS) is a universal concept for complex systems studies, which focuses on the volume of the basin of attraction instead of the traditional linearization-based approach. It has a lot of applications in real-world systems especially in dynamical systems with a phenomenon of multi-stability, which is even more ubiquitous in delayed dynamics such as the firing neurons, the climatological processes, and the power grids. Due to the infinite dimensional property of the space for the initial values, how to properly define the basin’s volume for delayed dynamics remains a fundamental problem. We propose here a technique which projects the infinite dimensional initial state space to a finite-dimensional Euclidean space by expanding the initial function along with different orthogonal or nonorthogonal basis. A generalized concept of basin’s volume in delayed dynamics and a highly practicable calculating algorithm with a cross-validation procedure are provided to numerically estimate the basin of attraction in delayed dynamics. We show potential applicabilities of this approach by applying it to study several representative systems of biological or/and physical significance, including the delayed Hopfield neuronal model with multistability and delayed complex networks with synchronization dynamics.
Sun, Miaoping; Nian, Xiaohong; Dai, Liqiong; Guo, Hua
2017-05-01
In this paper, the delay-dependent wide-area dynamic output feedback controller (DOFC) with prescribed degree of stability is proposed for interconnected power system to damp inter-area low-frequency oscillations. Here, the prescribed degree of stability α is used to maintain all the poles on the left of s=-α in the s-plane. Firstly, residue approach is adopted to select input-output control signals and the schur balanced truncation model reduction method is utilized to obtain the reduced power system model. Secondly, based on Lyapunov stability theory and transformation operation in complex plane, the sufficient condition of asymptotic stability for closed-loop power system with prescribed degree of stability α is derived. Then, a novel method based on linear matrix inequalities (LMIs) is presented to obtain the parameters of DOFC and calculate delay margin of the closed-loop system considering the prescribed degree of stability α. Finally, case studies are carried out on the two-area four-machine system, which is controlled by classical wide-area power system stabilizer (WAPSS) in reported reference and our proposed DOFC respectively. The effectiveness and advantages of the proposed method are verified by the simulation results under different operating conditions. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Absolute Stability for Lurie Control System with Unbound Time Delays
Institute of Scientific and Technical Information of China (English)
王天成; 王耀才; 洪留荣
2004-01-01
Time delay existes widely in various real engineering systems and can result in unsatisfactory performance or even an instability of control systems. Therefore, to investigate the stability for time delay systems is of vitul importance in control theory and its applications. Many researchers have studied the stability criteria of systems with constant delay or bound varying time delay, but few of them studied large time delay or unbound time delay. Large time delay existes commonly in various engineering applications. In this paper, the absolute stability of Lurie type direct control systems and indirect control systems with several time delays are discussed. Based on Lyapunov theory, the new delay dependent absolute stability criteria are derived. In our theorem, time delays can be unbound functions, which shows that the results are less conservative than that of existed criteria.
Delay-range-dependent stability for systems with time-varying delays%一类区间时变时滞系统的稳定性分析
Institute of Scientific and Technical Information of China (English)
但松健
2012-01-01
针对一类区间时变时滞系统的稳定性问题,进行了全局渐近稳定性分析.通过引入时滞分段方法和构建恰当的Lyapunov-Krasovskii泛函,得到了新的区间时滞相关稳定性判定准则.该准则以线性矩阵不等式形式给出,便于利用LMI工具箱对系统的稳定性进行判定.新准则具有较少的保守性,并且在一定范围内保守性随着时滞分段增多而减少,即时滞分段越多,保守性越少.数值仿真算结果例表明了新准则所具有的有效性和较少的保守性.%Aimed at the problem of the stability of systems with time-varying delay in a range, the global asymptotic stability a-nalysis of delay-range-dependent systems with time-varying delays is investigated. A new criterion of the delay-range-dependent stability is derived by introducing an appropriate type of Lyapunov-Krasovskii functional with the idea of delay fractioning and is formulated in terms of a linear matrix inequality (LMI), which can be readily solved via LMI Toolbox. This new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning within a certain range. Finally, a numerical example is given to demonstrate the effectiveness and the less conservative of the proposed criterion.
Li, Haiyin; Meng, Gang; She, Zhikun
In this paper, we investigate the stability and Hopf bifurcation of a delayed density-dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered such that the studied predator-prey system conforms to the realistically biological environment. We start with the geometric criterion introduced by Beretta and Kuang [2002] and then investigate the stability of the positive equilibrium and the stability switches of the system with respect to the delay parameter τ. Especially, we generalize the geometric criterion in [Beretta & Kuang, 2002] by introducing the condition (i‧) which can be assured by the condition (H2‧), and adopting the technique of lifting to define the function S˜n(τ) for alternatively determining stability switches at the zeroes of S˜n(τ)s. Afterwards, by the Poincaré normal form for Hopf bifurcation in [Kuznetsov, 1998] and the bifurcation formulae in [Hassard et al., 1981], we qualitatively analyze the properties for the occurring Hopf bifurcations of the system (3). Finally, an example with numerical simulations is given to illustrate the obtained results.
Institute of Scientific and Technical Information of China (English)
田俊康; 钟守铭; 熊良林
2008-01-01
This paper deals with delay-dependent robust stability of neutral Lurie control systems with multiple nonlinearities and time-varying structured uncertainties. The Lyapunov functional method is used. By adding some appropriate zero terms to the deviation of V and constructing some linear matrix inequalities, some sufficient conditions for the delay-dependent absolute stability and robust stability are derived. Finally, a numerical example is presented to illustrate the effectiveness of the method.
Analysis of Absolute Stability for Time-delay Teleoperation Systems
Institute of Scientific and Technical Information of China (English)
Qi-Wen Deng; Qing Wei; Ze-Xiang Li
2007-01-01
In this paper, a new bilateral control algorithm based on absolute stability theory is put forward, which aims at the time-delay teleoperation system with force feedback from the slave directly. In the new control algorithm, the delay-dependent stability,instead of delay-independent stability, is taken as the aim of control design. It improves the transparency of the system at the price of unnecessary stability. With this algorithm, the time-delay teleoperation systems have good transparency and stability. A simulation system is established to verify the effect of this algorithm.
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.
Lurie 控制系统的时滞相关绝对稳定性新判据%New Delay-dependent Absolute Stability Criteria for Lurie Control Systems
Institute of Scientific and Technical Information of China (English)
高金凤; 苏宏业; 嵇小辅; 褚健
2008-01-01
This note is concerned with the absolute stability analysis for time-delay Lurie control systems with nonlinearity located in an infinite sector and finite one. By using a new Lyapunov-Krasovskii functional that splits the whole delay interval into two subintervals and defines a different energy function on each subinterval and introducing some free-weighting matrices, some new delay-dependent robustly absolute stability criteria are presented in terms of strict linear matrix inequalities (LMIs). The obtained delay-dependent criteria are less conservative than previous ones, as arc illustrated by numerical examples.
Institute of Scientific and Technical Information of China (English)
程媛媛; 蒋威
2012-01-01
介绍了不确定时变时滞退化系统的一种新的鲁棒稳定性判据,该判据的提出利用适当的Lyapunov-Krasovskii函数方法,由一组线性矩阵不等式表示出来,判据可借助Matlab软件中LMI工具箱中得以验证.最后,数值实例证明了方法的有效性和优势.%This paper presents a new result of stability analysis for uncertain descriptor systems with time-varying delay,new delay-dependent robust stability criterion of uncertain time-delay descriptor systems is proposed by exploiting appropriate Lyapunov-Krasovskii functional candidate.This criterion is expressed by a set of linear matrix inequalities,which can be tested by using the LMI toolbox in Matlab.Finally,illustrative examples demonstrate the effectiveness and the advantage of the proposed method.
Global Asymplotic Stability of Neural Networks with Time Delay
Institute of Scientific and Technical Information of China (English)
肖晓丹; 张洁
2008-01-01
The global asymptotic stability problem of Cellular neural networks with delay is investigated.A new stability condition is presented based on Lyapunov-Krasovskii method,which is dependent On the size of delay.The result is given in the form of LMI.and the admitted upper bound of the delay can be obtained easily.The time delay dependent and independent results can be obtained,which include some results in the former literature.Finally,a numerical example is siven to illustrate the effectiveness of the main results.
Delay-dependent robust passivity control for uncertain time-delay systems
Institute of Scientific and Technical Information of China (English)
Li Guifang; Li Huiying; Yang Chengwu
2007-01-01
The robust passivity control problem is addressed for a class of uncertain delayed systems with timevarying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient condition is obtained for the nominal system, and then, based-on the former, the delay-dependent robust passivity criteria is provided and the corresponding controller is designed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the proposed approach.
Improved Stabilization Criteria for Neutral Time-Delay Systems
Lianglin Xiong; Haiyang Zhang; Yongkun Li; Zixin Liu
2016-01-01
This paper addresses the stabilization conditions for neutral systems with mixed time delays. By constructing a novel class of Lyapunov functionals which contains an augmented Lyapunov functional, using a new class of improved Jensen’s like inequalities, two improved delay-dependent stability criteria are firstly established. Next, state feedback controllers are designed according to the stability conditions in different cases. Finally, five numerical examples are provided to demonstrate the ...
Directory of Open Access Journals (Sweden)
Saffet Ayasun
2014-01-01
Full Text Available This paper investigates the effect of time delays on the stability of a generator excitation control system compensated with a stabilizing transformer known as rate feedback stabilizer to damp out oscillations. The time delays are due to the use of measurement devices and communication links for data transfer. An analytical method is presented to compute the delay margin for stability. The delay margin is the maximum amount of time delay that the system can tolerate before it becomes unstable. First, without using any approximation, the transcendental characteristic equation is converted into a polynomial without the transcendentality such that its real roots coincide with the imaginary roots of the characteristic equation exactly. The resulting polynomial also enables us to easily determine the delay dependency of the system stability and the sensitivities of crossing roots with respect to the time delay. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. Theoretical delay margins are computed for a wide range of controller gains and their accuracy is verified by performing simulation studies. Results indicate that the addition of a stabilizing transformer to the excitation system increases the delay margin and improves the system damping significantly.
Robust Stability Criterion for Uncertain Neural Networks with Time Delays
Institute of Scientific and Technical Information of China (English)
LIN Zhi-wei; ZHANG Ning; YANG Hong-jiu
2010-01-01
The robust stability of uncertain neural network with time-varying delay was investigated. The norm-bounded un-certainties are included in the system matrices. The constraint on time-varying delays is removed, which means that a fast time-varying delay is admissible. Some new delay-dependent stability criteria were presented by using Lyapunov-Krasovskii functional and linear matrix inequalities (LMIs) approaches. Finally, a numerical example was given to illustrate the effec-tiveness and innovation nature of the developed techniques.
New Results on Stability and Stabilization of Markovian Jump Systems with Time Delay
Directory of Open Access Journals (Sweden)
Hongwei Xia
2014-01-01
Full Text Available This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper.
Synchronization Stability in Weighted Complex Networks with Coupling Delays
Institute of Scientific and Technical Information of China (English)
WANG Qing-Yun; DUAN Zhi-Sheng; CHEN Guan-Rong; LU Qi-Shao
2009-01-01
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths.In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance.Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly ga/ns increasing attention in various fields of science and engineering.Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states.The obtained criteria in this paper encompass the established results in the literature as special cases.Some examples are given to illustrate the theoretical results.
Institute of Scientific and Technical Information of China (English)
张文安; 俞立
2007-01-01
This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discretedelay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.
Stabilization of a Nonlinear Delay System
Directory of Open Access Journals (Sweden)
Walid Arouri
2012-01-01
Full Text Available Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. Thats why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.
Delay-dependent H-infinity control for continuous time-delay systems via state feedback
Institute of Scientific and Technical Information of China (English)
Xinchun JIA; Yibo GAO; Jingmei ZHANG; Nanning ZHENG
2007-01-01
The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods of delay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.
Transcriptional delay stabilizes bistable gene networks
Gupta, Chinmaya; López, José Manuel; Ott, William; Josić, Krešimir; Bennett, Matthew R.
2014-01-01
Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner. PMID:23952450
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.
Dynamical output feedback stabilization for neutral systems with mixed delays
Institute of Scientific and Technical Information of China (English)
Wei QIAN; Guo-jiang SHEN; You-xian SUN
2008-01-01
This paper is concerned with the issue of stabilization for the linear neutral systems with mixed delays.The attention is focused on the design of output feedback controllers which guarantee the asymptotical stability of the closed-loop systems.Based on the model transformation of neutral type,the Lyapunov-Krasovskii functional method is employed to establish the delay-dependent stability criterion.Then,through the controller parameterization and some matrix transformation techniques,the desired parameters are determined under the delay-dependent design condition in terms of linear matrix inequalities (LMIs),and the desired controller is explicitly formulated.A numerical example is given to illustrate the effectiveness of the proposed method.
Delay-dependent robust H∞ control for uncertain discrete time-delay fuzzy systems
Institute of Scientific and Technical Information of China (English)
Gong Cheng; Su Baoku
2009-01-01
The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno (T-S) fuzzy tems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust H∞ controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.
New results on robust exponential stability of integral delay systems
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
Global exponential stability conditions for generalized state-space systems with time-varying delays
Energy Technology Data Exchange (ETDEWEB)
Yu, K.-W. [Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan (China)], E-mail: kwyu@mail.nkmu.edu.tw; Lien, C.-H. [Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan (China)], E-mail: chlien.ee@msa.hinet.net
2008-05-15
A unified approach is proposed to deal with the exponential stability for generalized state-space systems with time-varying delays. Many systems models can be regarded as special cases of the considered systems; such as neutral time-delay systems and delayed cellular neural networks. Delay-dependent stability criteria are proposed to guarantee the global exponential stability for generalized state-space systems with two cases of uncertainties. Two numerical examples are given to show the effectiveness of our method.
Energy Technology Data Exchange (ETDEWEB)
Yan, J.-J. [Department of Computer and Communication, Shu-Te University, Kaohsiung 824, Taiwan (China)]. E-mail: jjyan@mail.stu.edu.tw; Hung, M.-L. [Department of Electrical Engineering, Far-East College, No. 49, Jung-Haw Road, Hsin-Shih Town, Tainan 744, Taiwan (China)
2006-09-15
This paper investigates a novel stability criterion for interval time-delay chaotic systems via the evolutionary programming (EP) approach. First a delay-dependent criterion is derived for ensuring the stability of degenerate time-delay systems, and then by solving eigenvalue location optimization problems, which will be defined later, the robust stability of interval time-delay systems can be guaranteed. An example is given to verify our method that yields less conservative results than those appeared in the literature.
Logistic map with a delayed feedback: Stability of a discrete time-delay control of chaos.
Buchner, T; Zebrowski, J J
2001-01-01
The logistic map with a delayed feedback is studied as a generic model. The stability of the model and its bifurcation scheme is analyzed as a function of the feedback amplitude and of the delay. Stability analysis is performed semianalytically. A relation between the delay and the periodicity of the orbit, which explains why some terms used in chaos control are ineffective, was found. The consequences for chaos control are discussed. The structure of bifurcations is found to depend strongly on the parity and on the length of the delay. Boundary crisis, the tangent, the Neimark, as well as the period-doubling bifurcations occur in this system. The effective dimension of the model is also discussed.
THE ALL-DELAY STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAY
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper,the all-delay stability of degenerate differential systems with delay is discussed.We come up with some new criteria for evaluating the all-delay stability of degenerate differential systems with delay and degenerate neutral differential systems with delay.Also,we give an example to illustrate the main results.
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.
Institute of Scientific and Technical Information of China (English)
梁金玲; 黄霞
2005-01-01
Stability analysis of cellular neural networks (CNNs)has been an important topic in the neuralnetwork field since it has great significance for many applications. The qualitative analysis of the neurodynamics has attracted considerable attention thus far[1～7]. In electronic implementation of neural networks,many problems such as switching delays, integration, and communication delays have arisen. In such a case, a delay parameter must be introduced into the system model. Study of neural dynamics with consideration of delays becomes particularly important in manufacturing high quality microelectronic neural networks. Global stability of delayed cellular neural networks (DCNNs) has been extensively studied[1～11]. Sufficient conditions[5,9,12,13] for global stability of DCNNs have been proposed, but the output of the cell is a piecewise linear function and the time-delay is constant. A wider adaptive range without assuming the output of the cell to be piecewise linear function[10,13] is introduced and the time-delay terms of DCNNs are also constant.Based on the Lyapunov stability theorem as well as some facts about the negative definiteness and inequality of matrices, a new sufficient condition is presented for the existence of a unique equilibrium point and its global exponential stability of the delayed CNNs. This condition imposes constraints on the size of the delay parameter. An illustrative example and its numerical simulation is also given to show the effectiveness of our results.%细胞神经网络(CNNs)由于有许多重要的应用价值,所以它的稳定性分析一直是神经网络领域里的一个重要课题.近年来,神经动力系统的定性分析吸引了众多学者的关注[1-7].在神经网络的电子器件实现中,出现了许多问题,诸如:转换延时,积分器,连接延时等.在这种情况下,在系统模型中一定要引进一个延时参数.要制造高质量的微电子神经网络,研究带有延时的神经动
Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems
Institute of Scientific and Technical Information of China (English)
Nam PHAN T.; Phat VU N.
2008-01-01
This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems.The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities(LMIs)and we develop control design methods based on UMIs for solving stabilization problem.Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov funcfionals,which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution.Numerical examples illustrating the conditions are given.
On exponential stability for systems with state delays
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper considers the issue of delay-dependent exponential stability for time-delay systems. Both nominal and uncertain systems are investigated. New sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained. These criteria are simple owing to the use of an integral inequality. The model transformation approaches, bounding techniques for cross terms and slack matrices are all avoided in the derivation. Rigorous proof and numerical examples showed that the proposed criteria and those based on introducing slack matrices are equivalent.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on an appropriate Lyapunov function,this paper analyzes the design of a delay-dependent robust H∞ state feedback control,with a focus on a class of non linear uncertainty linear time-delay systems with input delay using linear matrix inequalities.Under the condition that the nonlinear uncertain functions are gain bounded,a sufficient condition dependent on the delays of the state and input is presented for the existence of H∞ controller.The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H∞ norm bound of closed-loop transfer matrix from the disturbance to controlled output.By solving a linear matrix inequation,we can obtain the robust H∞ controller.An example is given to show the effectiveness of the proposed method.
New asymptotic stability criteria for neural networks with time-varying delay
Energy Technology Data Exchange (ETDEWEB)
Tian Junkang, E-mail: tianjunkang1980@163.co [School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500 (China); Xie Xiangjun [School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500 (China)
2010-02-01
The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.
Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays
Directory of Open Access Journals (Sweden)
Xiaofeng Chen
2014-01-01
Full Text Available The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global μ-stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.
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 and Stabilization of Networked Control System with Forward and Backward Random Time Delays
Directory of Open Access Journals (Sweden)
Ye-Guo Sun
2012-01-01
Full Text Available This paper deals with the problem of stabilization for a class of networked control systems (NCSs with random time delay via the state feedback control. Both sensor-to-controller and controller-to-actuator delays are modeled as Markov processes, and the resulting closed-loop system is modeled as a Markovian jump linear system (MJLS. Based on Lyapunov stability theorem combined with Razumikhin-based technique, a new delay-dependent stochastic stability criterion in terms of bilinear matrix inequalities (BMIs for the system is derived. A state feedback controller that makes the closed-loop system stochastically stable is designed, which can be solved by the proposed algorithm. Simulations are included to demonstrate the theoretical result.
Exponential Stability of Uncertain T-S Fuzzy Switched Systems with Time Delay
Institute of Scientific and Technical Information of China (English)
Fatima Ahmida; El Houssaine Tissir
2013-01-01
This paper discusses the delay-dependent exponential stability of a class of uncertain T-S fuzzy switched systems with time delay.The method is based on Lyapunov stability theorem and free weighting matrices approach.Two illustrative examples are given to demonstrate the effectiveness of the proposed method.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
Delay-dependent H-infinity filtering for neutral time-delay systems
Institute of Scientific and Technical Information of China (English)
Huiying LI; Guifang LI; Chengwu YANG
2006-01-01
This paper deals with the robust delay-dependent H-infinity filtering problem for neutral delay differential systems. The resulting filter is of the Luenberger observer type, and it guarantees that the filtering systems remains asymptotically stable and satisfies a prescribed H-infinity performance level. The Lyapunov stability theory and the descriptor model transformation are used for analysis of the system and are expected to be least conservative as compared with existing design methods. Some examples are provided to demonstrate the validity of proposed design approach.
Delay-dependent robust H∞ control of convex polyhedral uncertain fuzzy systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with time-varying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities (LMIs). For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.
Texting Dependence, iPod Dependence, and Delay Discounting.
Ferraro, F Richard; Weatherly, Jeffrey N
2016-01-01
We gave 127 undergraduates questionnaires about their iPod and texting dependence and 2 hypothetical delay discounting scenarios related to free downloaded songs and free texting for life. Using regression analyses we found that when iPod dependence was the dependent variable, Text2-excessive use, Text4-psychological and behavioral symptoms, iPod2-excessive use, and iPod3-relationship disruption were significant predictors of discounting. When texting dependence was the dependent variable, Text4-psychological and behavioral symptoms and iPod3-relationship disruption were significant predictors of discounting. These are the first data to show that delay discounting relates to certain aspects of social media, namely iPod and texting dependence. These data also show that across these 2 dependencies, both psychological and behavioral symptoms and relationship disruptions are affected.
Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays
Directory of Open Access Journals (Sweden)
Manlika Rajchakit
2012-01-01
Full Text Available This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.
Institute of Scientific and Technical Information of China (English)
Xianming ZHANG; Min WU; Jinhua SHE; Dongsheng HAN
2006-01-01
This paper examines the delay-dependent H-infinity control problem for discrete-time linear systems with time-varying state delays and norm-bounded uncertainties. A new inequality for the finite sum of quadratic terms is first established. Then, some new delay-dependent criteria are derived by employing the new inequality to guarantee the robust stability of a closed-loop system with a prescribed H-infinity norm bound for all admissible uncertainties and bounded time-vary delays. A numerical example demonstrates that the proposed method is an improvement over existing ones.
Zhou, Liqun; Zhang, Yanyan
2016-01-01
In this paper, a class of recurrent neural networks with multi-proportional delays is studied. The nonlinear transformation transforms a class of recurrent neural networks with multi-proportional delays into a class of recurrent neural networks with constant delays and time-varying coefficients. By constructing Lyapunov functional and establishing the delay differential inequality, several delay-dependent and delay-independent sufficient conditions are derived to ensure global exponential periodicity and stability of the system. And several examples and their simulations are given to illustrate the effectiveness of obtained results.
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.
Chen, Huabin; Shi, Peng; Lim, Cheng-Chew; Hu, Peng
2016-06-01
In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.
Simultaneous quadratic performance stabilization for linear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Yuepeng; Zhou Zude; Liu Huanbin; Zhang Qingling
2006-01-01
A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities (LMIs) which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.
Stabilizing unstable steady states using multiple delay feedback control.
Ahlborn, Alexander; Parlitz, Ulrich
2004-12-31
Feedback control with different and independent delay times is introduced and shown to be an efficient method for stabilizing fixed points (equilibria) of dynamical systems. In comparison to other delay based chaos control methods multiple delay feedback control is superior for controlling steady states and works also for relatively large delay times (sometimes unavoidable in experiments due to system dead times). To demonstrate this approach for stabilizing unstable fixed points we present numerical simulations of Chua's circuit and a successful experimental application for stabilizing a chaotic frequency doubled Nd-doped yttrium aluminum garnet laser.
Robust stability of uncertain neutral linear stochastic differential delay system
Institute of Scientific and Technical Information of China (English)
JIANG Ming-hui; SHEN Yi; LIAO Xiao-xin
2007-01-01
The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.
New Stability Conditions for Linear Differential Equations with Several Delays
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2011-01-01
Full Text Available New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation x˙(t+∑k=1mak(tx(hk(t=0 with measurable delays and coefficients. These results are compared to known stability tests.
Nonuniform behavior and stability of Hopfield neural networks with delay
Bento, António J. G.; Oliveira, José J.; Silva, César M.
2017-08-01
Based on a new abstract result on the behavior of nonautonomous delayed equations, we obtain a stability result for the solutions of a general discrete nonautonomous Hopfield neural network model with delay. As an application we improve some existing results on the stability of Hopfield models.
Stability analysis of a class of fractional delay differential equations
Indian Academy of Sciences (India)
Sachin B Bhalekar
2013-08-01
In this paper we analyse stability of nonlinear fractional order delay differential equations of the form $D^{} y(t) = af(y(t - )) - {\\text{by}} (t)$, where $D^{}$ is a Caputo fractional derivative of order 0 < ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic equation with delay.
Global asymptotic stability of cellular neural networks with multiple delays
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
The K-Stability of Nonlinear Delay Systems
Institute of Scientific and Technical Information of China (English)
章毅; 张毅; 王联
1994-01-01
In this paper,we study the K-stability theory of nonlinear delay systems.In the more general case,we establish two nonlinear delay differential inequalities.Therefore,to study the X-stability,a powerful method is provided.By making use of the foregoing inequalities,we analyse and investigate some K-stabiiity conditions of nonlinear delay systems.Finally,some examples are given to illustrate our theory.
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.
Stability of Non-Neutral and Neutral Dynamic Switched Systems Subject to Internal Delays
Directory of Open Access Journals (Sweden)
M. De la Sen
2005-01-01
Full Text Available This study deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky-Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems.
Directory of Open Access Journals (Sweden)
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
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.
Stability interval for time-varying delay systems
Ariba, Yassine; Gouaisbaut, F.; Johansson, Karl Henrik
2010-01-01
We investigate the stability analysis of linear time-delay systems. The time-delay is assumed to be a time-varying continuous function belonging to an interval (possibly excluding zero) with a bound on its derivative. To this end, we propose to use the quadratic separation framework to assess the intervals on the delay that preserves the stability. Nevertheless, to take the time-varying nature of the delay into account, the quadratic separation principle has to be extended to cope with the ge...
Stabilization of a Class of Stochastic Systems with Time Delays
Directory of Open Access Journals (Sweden)
Jian Wang
2014-01-01
Full Text Available The problem of exponential stability is investigated for a class of stochastic time-delay systems. By using the decomposition technique and Lyapunov stability theory, two improved exponential stability criteria are derived. Finally, a numerical example is given to illustrate the effectiveness and the benefit of the proposed method.
Institute of Scientific and Technical Information of China (English)
Weihai ZHANG; Xuezhen LIU; Shulan KONG; Qinghua LI
2006-01-01
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
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.
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.
Stability of discrete Hopfield neural networks with delay
Institute of Scientific and Technical Information of China (English)
Ma Runnian; Lei Sheping; Liu Naigong
2005-01-01
Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network's applications. The stability of discrete Hopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.
Directory of Open Access Journals (Sweden)
Jinxing Lin
2013-01-01
Full Text Available This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs, delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.
Stability of neutral equations with constant time delays
Barker, L. K.; Whitesides, J. L.
1976-01-01
A method was developed for determining the stability of a scalar neutral equation with constant coefficients and constant time delays. A neutral equation is basically a differential equation in which the highest derivative appears both with and without a time delay. Time delays may appear also in the lower derivatives or the independent variable itself. The method is easily implemented, and an illustrative example is presented.
H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay
Institute of Scientific and Technical Information of China (English)
Bai-Da Qu
2005-01-01
In this paper,H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.
Directory of Open Access Journals (Sweden)
Zhang Xinhua
2011-01-01
Full Text Available Abstract In this paper, a class of impulsive bidirectional associative memory (BAM fuzzy cellular neural networks (FCNNs with time delays in the leakage terms and distributed delays is formulated and investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time delays in the leakage terms and distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.
Razumikhin Stability Theorem for Fractional Systems with Delay
Directory of Open Access Journals (Sweden)
D. Baleanu
2010-01-01
Full Text Available Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
STABILITY OF TIME VARYING SINGULAR DIFFERENTIAL SYSTEMS WITH DELAY
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.
Delay-independent stability of genetic regulatory networks.
Wu, Fang-Xiang
2011-11-01
Genetic regulatory networks can be described by nonlinear differential equations with time delays. In this paper, we study both locally and globally delay-independent stability of genetic regulatory networks, taking messenger ribonucleic acid alternative splicing into consideration. Based on nonnegative matrix theory, we first develop necessary and sufficient conditions for locally delay-independent stability of genetic regulatory networks with multiple time delays. Compared to the previous results, these conditions are easy to verify. Then we develop sufficient conditions for global delay-independent stability for genetic regulatory networks. Compared to the previous results, this sufficient condition is less conservative. To illustrate theorems developed in this paper, we analyze delay-independent stability of two genetic regulatory networks: a real-life repressilatory network with three genes and three proteins, and a synthetic gene regulatory network with five genes and seven proteins. The simulation results show that the theorems developed in this paper can effectively determine the delay-independent stability of genetic regulatory networks.
Directory of Open Access Journals (Sweden)
Haiyang Zhang
2016-01-01
Full Text Available This paper is concerned with the problem of delay-dependent stability of time-delay systems. Firstly, it introduces a new useful integral inequality which has been proved to be less conservative than the previous inequalities. Next, the inequality combines delay-decomposition approach with uncertain parameters applied to time-delay systems, based on the new Lyapunov-Krasovskii functionals and new stability criteria for system with time-delay have been derived and expressed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness and the less conservative feature of the proposed method compared with some recent results.
Stability of a delayed predator—prey model in a random environment
Jin, Yan-Fei; Xie, Wen-Xian
2015-11-01
The stability of the first-order and second-order solution moments for a Harrison-type predator-prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Itô interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results. Project supported by the National Natural Science Foundation of China (Grant Nos. 11272051 and 11302172).
Stability of a delayed predator prey model in a random environment
Institute of Scientific and Technical Information of China (English)
靳艳飞; 谢文贤
2015-01-01
The stability of the first-order and second-order solution moments for a Harrison-type predator–prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Itˆo interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.
GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS
Institute of Scientific and Technical Information of China (English)
ZHOU Dong-ming; CAO Jin-de; ZHANG Li-ming
2005-01-01
Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore, the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.
Stability criteria for linear systems with multiple time-varying delays
Institute of Scientific and Technical Information of China (English)
Bugong XU
2003-01-01
New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the me-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast me-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature.
Ahn, Choon Ki; Shi, Peng; Wu, Ligang
2015-12-01
This paper is concerned with the problems of receding horizon stabilization and disturbance attenuation for neural networks with time-varying delay. New delay-dependent conditions on the terminal weighting matrices of a new finite horizon cost functional for receding horizon stabilization are established for neural networks with time-varying or time-invariant delays using single- and double-integral Wirtinger-type inequalities. Based on the results, delay-dependent sufficient conditions for the receding horizon disturbance attenuation are given to guarantee the infinite horizon H∞ performance of neural networks with time-varying or time-invariant delays. Three numerical examples are provided to illustrate the effectiveness of the proposed approach.
Stabilizing control for a class of delay unstable processes.
Lee, See Chek; Wang, Qing-Guo; Nguyen, Le Binh
2010-07-01
The stabilization of unstable first-order plus time-delay processes with a zero by means of simple controllers is investigated in detail. Explicit stabilizability conditions are established. And the computational methods for determining stabilizing controller parameters are also presented with illustrative examples.
Absolute Stability of Discrete-Time Systems with Delay
Directory of Open Access Journals (Sweden)
Medina Rigoberto
2008-01-01
Full Text Available We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the "freezing" technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.
Finite-Time Stability of Nonautonomous Delayed Systems
Institute of Scientific and Technical Information of China (English)
孙武军; 孔德兴
2003-01-01
The finite-time stability to linear discontinuous time-varying delayed system was investigated. By applying the method of upper and lower solutions, some sufficient conditions of this kind of stability were obtained.Furthermore, it also developed a monotone iterative technique for obtaining solutions which are obtained as limits of monotone sequences
ASYMPTOTIC STABILITY OF A SINGULAR SYSTEM WITH DISTRIBUTED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
GLOBAL STABILITY IN HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED TIME DELAYS
Institute of Scientific and Technical Information of China (English)
Zhang Jiye; Wu Pingbo; Dai Huanyun
2001-01-01
In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.
STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we obtain suffcient conditions for the stability in p-th moment of the analytical solutions and the mean square stability of a stochastic differential equation with unbounded delay proposed in [6,10] using the explicit Euler method.
Directory of Open Access Journals (Sweden)
J. Thipcha
2013-01-01
Full Text Available The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI. Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Numerical Stability Test of Neutral Delay Differential Equations
Directory of Open Access Journals (Sweden)
Z. H. Wang
2008-01-01
Full Text Available The stability of a delay differential equation can be investigated on the basis of the root location of the characteristic function. Though a number of stability criteria are available, they usually do not provide any information about the characteristic root with maximal real part, which is useful in justifying the stability and in understanding the system performances. Because the characteristic function is a transcendental function that has an infinite number of roots with no closed form, the roots can be found out numerically only. While some iterative methods work effectively in finding a root of a nonlinear equation for a properly chosen initial guess, they do not work in finding the rightmost root directly from the characteristic function. On the basis of Lambert W function, this paper presents an effective iterative algorithm for the calculation of the rightmost roots of neutral delay differential equations so that the stability of the delay equations can be determined directly, illustrated with two examples.
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.
Temperature Dependent Wire Delay Estimation in Floorplanning
DEFF Research Database (Denmark)
Winther, Andreas Thor; Liu, Wei; Nannarelli, Alberto;
2011-01-01
Due to large variations in temperature in VLSI circuits and the linear relationship between metal resistance and temperature, the delay through wires of the same length can be different. Traditional thermal aware floorplanning algorithms use wirelength to estimate delay and routability. In this w......Due to large variations in temperature in VLSI circuits and the linear relationship between metal resistance and temperature, the delay through wires of the same length can be different. Traditional thermal aware floorplanning algorithms use wirelength to estimate delay and routability...
Angular dependence of Wigner time delay: Relativistic Effects
Mandal, A.; Deshmukh, P. C.; Manson, S. T.; Kkeifets, A. S.
2016-05-01
Laser assisted photoionization time delay mainly consists of two parts: Wigner time delay, and time delay in continuum-continuum transition. Wigner time delay results from the energy derivative of the phase of the photoionization amplitude (matrix element). In general, the photoionization time delay is not the same in all directions relative to the incident photon polarization, although when a single transition dominates the amplitude, the resultant time delay is essentially isotropic. The relativistic-random-phase approximation is employed to determine the Wigner time delay in photoionization from the outer np subshells of the noble gas atoms, Ne through Xe. The time delay is found to significantly depend on angle, as well as energy. The angular dependence of the time delay is found to be quite sensitive to atomic dynamics and relativistic effects, and exhibit strong energy and angular variation in the neighborhood of Cooper minima. Work supported by DOE, Office of Chemical Sciences and DST (India).
Delay-Dependent Observers for Uncertain Nonlinear Time-Delay Systems
Directory of Open Access Journals (Sweden)
Dongmei Yan
2013-05-01
Full Text Available This paper is concerned with the observer design problem for a class of discrete-time uncertain nonlinear systems with time-varying delay. The nonlinearities are assumed to satisfy global Lipschitz conditions which appear in both the state and measurement equations. The uncertainties are assumed to be time-varying but norm-bounded. Two Luenberger-like observers are proposed. One is delay observer and the other is delay-free observer. The delay observer which has an internal time delay is applicable when the time delay is known. The delay-free observer which does not use delayed information is especially applicable when the time delay is not known explicitly. Delay-dependent conditions for the existences of these two observers are derived based on Lyapunpv functional approach. Based on these conditions, the observer gains are obtained using the cone complementarity linearization algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Phase-locked solutions and their stability in the presence of propagation delays
Indian Academy of Sciences (India)
Gautham C Sethia; Abhijit Sen; Fatihcan M Atay
2011-11-01
We investigate phase-locked solutions of a continuum ﬁeld of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and travelling wave solutions in the parameter space characterizing the nonlocality and time delay are delineated. For the synchronous states a comprehensive stability diagram is presented that provides a heuristic synchronization condition as well as an analytic relation for the marginal stability curve. The relation yields simple stability expressions in the limiting cases of local and global coupling of phase oscillators.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
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.
Relativistic calculations of angular dependent photoemission time delay
Kheifets, A S; Deshmukh, P C; Dolmatov, V K; Manson, S T
2016-01-01
Angular dependence of photoemission time delay for the valence $np_{3/2}$ and $np_{1/2}$ subshells of Ar, Kr and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.
Relativistic calculations of angle-dependent photoemission time delay
Kheifets, Anatoli; Mandal, Ankur; Deshmukh, Pranawa C.; Dolmatov, Valeriy K.; Keating, David A.; Manson, Steven T.
2016-07-01
Angular dependence of photoemission time delay for the valence n p3 /2 and n p1 /2 subshells of Ar, Kr, and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.
Global exponential stability for switched memristive neural networks with time-varying delays.
Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia
2016-08-01
This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.
Stability domains of the delay and PID coefficients for general time-delay systems
Almodaresi, Elham; Bozorg, Mohammad; Taghirad, Hamid D.
2016-04-01
Time delays are encountered in many physical systems, and they usually threaten the stability and performance of closed-loop systems. The problem of determining all stabilising proportional-integral-derivative (PID) controllers for systems with perturbed delays is less investigated in the literature. In this study, the Rekasius substitution is employed to transform the system parameters to a new space. Then, the singular frequency (SF) method is revised for the Rekasius transformed system. A novel technique is presented to compute the ranges of time delay for which stable PID controller exists. This stability range cannot be readily computed from the previous methods. Finally, it is shown that similar to the original SF method, finite numbers of singular frequencies are sufficient to compute the stable regions in the space of time delay and controller coefficients.
Stability Analysis of a Class of Three-Neuron Delayed Cellular Neural Network
Directory of Open Access Journals (Sweden)
Poulami D. Gupta
2010-01-01
Full Text Available Problem statement: In this study linear stability of a class of three neuron cellular network with transmission delay had been studied. Approach: The model for the problem was first presented. The problem is then formulated analytically and numerical simulations pertaining to the model are carried out. Results: A necessary and sufficient condition for asymptotic stability of trivial steady state in the absence of delay is derived. Then a delay dependent sufficient condition for local asymptotic stability of trivial, steady state and sufficient condition for no stability switching of trivial steady for such a network are derived. Numerical simulation results of the model were presented. Conclusion/Recommendations: From numerical simulation, it appears that there may be a possibility of multiple steady states of the model. It may be possible to investigate the condition for the existence of periodic solutions of the non-linear model analytically.
Robust Stabilization for Uncertain Linear Delay Markow Jump System
Institute of Scientific and Technical Information of China (English)
钟麦英; 汤兵勇; 黄小原
2001-01-01
Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.
Absolute Stability of Discrete-Time Systems with Delay
Directory of Open Access Journals (Sweden)
Rigoberto Medina
2008-02-01
Full Text Available We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the Ã¢Â€ÂœfreezingÃ¢Â€Â technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.
New Stability Criteria for High-Order Neural Networks with Proportional Delays
Xu, Chang-Jin; Li, Pei-Luan
2017-03-01
This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation {y}i(t)={u}i({{{e}}}t){{ }}(i=1,2,\\ldots ,n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and time-varying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results. Supported by National Natural Science Foundation of China under Grant Nos. 61673008 and 11261010, and Project of High-level Innovative Talents of Guizhou Province ([2016]5651)
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.
Institute of Scientific and Technical Information of China (English)
徐瑞; 封汉颍; 阳平华; 王志强
2002-01-01
A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate co nditions,and sufficient conditions are obtained for the local asymptotic stabili ty of a positive equilibrium of the system.
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.
STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY
Institute of Scientific and Technical Information of China (English)
王林山; 徐道义
2002-01-01
The global asymptotic stability for Hopfield neural networks with time delay was investigated. A theorem and two corollaries were obtained, in which the boundedness and differentiability offjon R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.
Stability and Relative Stability of Linear Systems with Many Constant Time Delays. Ph.D. Thesis
Barker, Larry Keith
1976-01-01
A method of determining the stability of linear systems with many constant time delays is developed. This technique, an extension of the tau-decomposition method, is used to examine not only the stability but also the relative stability of retarded systems with many delays and a class of neutral equations with one delay. Analytical equations are derived for partitioning the delay space of a retarded system with two time delays. The stability of the system in each of the regions defined by the partitioning curves in the parameter plane is determined using the extended tau-decomposition method. In addition, relative stability boundaries are defined using the extended tau-decompositon method in association with parameter plane techniques. Several applications of the extended tau-decomposition method are presented and compared with stability results obtained from other analyses. In all cases the results obtained using the method outlined herein coincide with and extend those of previous investigations. The extended tau-decomposition method applied to systems with time delays requires less computational effort and yields more complete stability analyses than previous techniques.
Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate.
Huang, Gang; Takeuchi, Yasuhiro; Ma, Wanbiao; Wei, Daijun
2010-07-01
In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, we prove the global stability of the endemic equilibrium and the disease-free equilibrium for time delays of any length in each model. Our results show that the global properties of equilibria also only depend on the basic reproductive number and that the latent period in a vector does not affect the stability, but the latent period in an infected host plays a positive role to control disease development.
Directory of Open Access Journals (Sweden)
Xia Zhou
2013-01-01
Full Text Available The problem of bounded-input bounded-output (BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs, whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained 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.
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.
The range of time delay and the global stability of the equilibrium for an IVGTT model☆
Li, Jiaxu; Wang, Minghu; De Gaetano, Andrea; Palumbo, Pasquale; Panunzi, Simona
2011-01-01
Diabetes mellitus has become a prevalent disease in the world. Diagnostic protocol for the onset of diabetes mellitus is the initial step in the treatments. The intravenous glucose tolerance test (IVGTT) has been considered as the most accurate method to determine the insulin sensitivity and glucose effectiveness. It is well known that there exists a time delay in insulin secretion stimulated by the elevated glucose concentration level. However, the range of the length of the delay in the existing IVGTT models are not fully discussed and thus in many cases the time delay may be assigned to a value out of its reasonable range. In addition, several attempts had been made to determine when the unique equilibrium point is globally asymptotically stable. However, all these conditions are delay-independent. In this paper, we discuss the range of the time delay and provide easy-to-check delay-dependent conditions for the global asymptotic stability of the equilibrium point for a recent IVGTT model through Liapunov function approach. Estimates of the upper bound of the delay for global stability are given in corollaries. In addition, the numerical simulation in this paper is fully incorporated with functional initial conditions, which is natural and more appropriate in delay differential equation system. PMID:22123436
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.
A new delay-independent condition for global robust stability of neural networks with time delays.
Samli, Ruya
2015-06-01
This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results.
Delay-dependent guaranteed cost control for uncertain systems with both state and input delays
Institute of Scientific and Technical Information of China (English)
Xuanfang YANG; Wuhua CHEN; Huajing FANG
2004-01-01
This paper considers the guaranteed cost control problem for a class of uncertain linear systems with both state and input delays.By representing the time-delay system in the descriptor system form and using a recent result on bounding of cross products of vectors,we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost controller in terms of linear matrix inequalities.Two examples are presented which show the effectiveness of our approach.
State-dependent neutral delay equations from population dynamics.
Barbarossa, M V; Hadeler, K P; Kuttler, C
2014-10-01
A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.
Stability analysis in a car-following model with reaction-time delay and delayed feedback control
Jin, Yanfei; Xu, Meng
2016-10-01
The delayed feedback control in terms of both headway and velocity differences has been proposed to guarantee the stability of a car-following model including the reaction-time delay of drivers. Using Laplace transformation and transfer function, the stable condition is derived and appropriate choices of time delay and feedback gains are designed to stabilize traffic flow. Meanwhile, an upper bound on explicit time delay is determined with respect to the response of desired acceleration. To ensure the string stability, the explicit time delay cannot over its upper bound. Numerical simulations indicate that the proposed control method can restraint traffic congestion and improve control performance.
Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays.
Ndongo, Abdoul Samba; Talibi Alaoui, Hamad
2014-01-01
In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T, V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R 0 and R 1 which depends on the delays.
Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays
2014-01-01
In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T, V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R 0 and R 1 which depends on the delays. PMID:27355007
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.
Hopf bifurcation of a ratio-dependent predator-prey system with time delay
Energy Technology Data Exchange (ETDEWEB)
Celik, Canan [TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Soeguetoezue 06560, Ankara (Turkey)], E-mail: canan.celik@etu.tr
2009-11-15
In this paper, we consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.
Control of time stability of scintillation spectrometer of delayed coincidences
Morozov, V A
2002-01-01
Paper describes a system to control time stability of a two-detector plastic scintillation spectrometer of three-dimensional coincides. A two-reference control system incorporates a light guide base delay optical line, two light diodes and a two-channel generator of nanosecond pulses. A distinguishing feature of the design system is application of one delay line to form both advance and delay time signal as to the real coincidences in the studied radioactive source. The designed system of control enables to measure periods of half-decay of nuclei excited states within 40-100 ns range ensuring control of position of coincidence curve gravity centers within 4 ps limits
Delay-dependent robust H∞ control for uncertain fuzzy hyperbolic systems with multiple delays
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The robust H∞ control problem was considered for a class of fuzzy hyperbolic model (FHM) systems with parametric uncertainties and multiple delays. First, FHM modeling method was presented for time-delay nonlinear systems. Then, by using Lyapunov-Krasovskii approaches, delay-dependent sufficient condition for the existence of a kind of state feedback controller was proposed, which was expressed as linear matrix inequalities (LMIs). The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level for all admissible uncertainties and time-delay. Finally, a simulation example was provided to illustrate the effectiveness of the proposed approach.
Stability and persistence in plankton models with distributed delays
Abdallah, S H
2003-01-01
In this paper a model with two independent distributed delays is proposed to describe a population of microorganism feeding on a limiting nutrient which is supplied at a constant rate and is recycled after the death of the species by decomposer action. We obtain sufficient conditions for local and global stability of the positive equilibrium of the model. A fairly general function for nutrient uptake is considered. Stability changes of the positive equilibrium as the nutrient supply increases are studied by the Hopf bifurcation theorem.
Stability analysis of linear multistep methods for delay differential equations
Directory of Open Access Journals (Sweden)
V. L. Bakke
1986-01-01
Full Text Available Stability properties of linear multistep methods for delay differential equations with respect to the test equation y′(t=ay(λt+by(t, t≥0,0<λ<1, are investigated. It is known that the solution of this equation is bounded if and only if |a|<−b and we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams methods.
Oscillation and stability of delay models in biology
Agarwal, Ravi P; Saker, Samir H
2014-01-01
Environmental variation plays an important role in many biological and ecological dynamical systems. This monograph focuses on the study of oscillation and the stability of delay models occurring in biology. The book presents recent research results on the qualitative behavior of mathematical models under different physical and environmental conditions, covering dynamics including the distribution and consumption of food. Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.
Institute of Scientific and Technical Information of China (English)
Jinxing Lin; Shumin Fei; Jiong Shen
2010-01-01
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities(LMIs).An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms(ignored in previous methods)when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.
Robust delay-dependent feedforward control of neutral time-delay systems via dynamic IQCs
Ucun, L.; Küçükdemiral, I. B.
2014-05-01
This paper studies the design problem of delay-dependent ? based robust and optimal feedforward controller design for a class of time-delay control systems having state, control and neutral type delays which are subject to norm-bounded uncertainties and ? type measurable or observable disturbance signals. Two independent loops which include state-feedback and dynamic feedforward controller form the basis of the proposed control scheme in this study. State-feedback controller is generally used in stabilisation of the nominal delay-free system, whereas the feedforward controller is used for improving disturbance attenuation performance of the overall system. In order to obtain less conservative results, the delay and parametric uncertainty effects are treated in operator view point and represented by frequency-dependent (dynamic) integral quadratic constraints (IQCs). Moreover, sufficient delay-dependent criterion is developed in terms of linear matrix inequalities (LMIs) such that the time-delay system having parametric uncertainties is guaranteed to be asymptotically stable with minimum achievable disturbance attenuation level. Plenty of numerical examples are provided at the end, in order to illustrate the efficiency of the proposed technique. The achieved results on minimum achievable disturbance attenuation level and maximum allowable delay bounds are exhibited to be less conservative in comparison to those of controllers having only feedback loop.
Directory of Open Access Journals (Sweden)
Shengwei Yao
2014-01-01
Full Text Available A FitzHugh-Nagumo (FHN neural system with multiple delays has been proposed. The number of equilibrium point is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the saddle-node bifurcation of nontrivial equilibrium point and transcritical bifurcation of trivial one. Further, the stability of equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving the multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independence and delay-dependence stability. Increasing delay induces the stability switching between resting state and periodic activity in some parameter regions of coupling weight. Finally, numerical simulations are taken to support the theoretical results.
Delay-Dependent H∞ Filtering for Singular Time-Delay Systems
Directory of Open Access Journals (Sweden)
Zhenbo Li
2011-01-01
Full Text Available This paper deals with the problem of delay-dependent H∞ filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribed H∞ performance γ is given in terms of linear matrix inequalities (LMIs. Then, the sufficient condition is obtained for the existence of the H∞ filter, and the explicit expression for the desired H∞ filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.
Liu, Yuzhi; Li, Muguo
2015-05-01
This paper investigates the robust stabilization problem for uncertain linear systems with interval time-varying delays. By constructing novel Lyapunov-Krasovskii functionals and developing delay-partitioning approaches, some delay-dependent stability criteria are derived based on an improved Wirtinger׳s inequality and the reciprocally convex method. The proposed methods have improved the stability conditions without increasing much computational complexity. A state feedback controller design approach is also presented based on the proposed criteria. Numerical examples are finally given to illustrate the effectiveness of the proposed method.
Global asymptotic stability of positive equilibrium in a 3-species cooperating model with time delay
Institute of Scientific and Technical Information of China (English)
WANG Chang-you
2007-01-01
The asymptotic behavior of the time-dependent solution for a 3-species cooperating model was investigated with the effects of both diffusion and time delay taken into consideration. We proved the global asymptotic stability of a positive steady-state solution to the model problem by using coupled upper and lower solutions for a more general reaction-diffusion system that gives a common framework for 3-species cooperating model problems. The result of global asymptotic stability implies that the model system coexistence is permanent. Some global asymptotic stability results for 2-species cooperating reaction-diffusion systems are included in the discussion, and some known results are extended.
Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays
Directory of Open Access Journals (Sweden)
Tadeusz Kaczorek
2013-06-01
Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.
Bifurcation and chaos in a ratio-dependent predator-prey system with time delay
Energy Technology Data Exchange (ETDEWEB)
Gan Qintao [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China)], E-mail: ganqintao@sina.com; Xu Rui [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China); Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China); Yang Pinghua [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China)
2009-02-28
In this paper, a ratio-dependent predator-prey model with time delay is investigated. We first consider the local stability of a positive equilibrium and the existence of Hopf bifurcations. By using the normal form theory and center manifold reduction, we derive explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions. Finally, we consider the effect of impulses on the dynamics of the above time-delayed population model. Numerical simulations show that the system with constant periodic impulsive perturbations admits rich complex dynamic, such as periodic doubling cascade and chaos.
Karafyllis, Iasson
2010-01-01
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under th...
Delay-dependent passive control of linear systems with nonlinear perturbation
Institute of Scientific and Technical Information of China (English)
Li Caina; Cui Baotong
2008-01-01
The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive.In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity.Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities (LMIs). In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.
2-D algebraic test for robust stability of time-delay systems with interval parameters
Institute of Scientific and Technical Information of China (English)
Xiao Yang
2006-01-01
The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional (2-D) interval polynomials (2-D s-z hybrid polynomials), proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.
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...
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.
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.
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
STABILITY OF N-DIMENSIONAL LINEAR SYSTEMS WITH MULTIPLE DELAYS AND APPLICATION TO SYNCHRONIZATION
Institute of Scientific and Technical Information of China (English)
Weihua DENG; Jinhu L(U); Changpin LI
2006-01-01
This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore (2002). Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua's systems.
Hyong Koh, M; Sipahi, Rifat
2016-11-01
Dynamics of many multi-agent systems is influenced by communication/activation delays τ. In the presence of delays, there exists a certain margin called the delay margin τ(*), less than which system stability holds. This margin depends strongly on agents' dynamics and the agent network. In this article, three key elements, namely, the delay margin, network graph, and a distance threshold conditioning two agents' connectivity are considered in a multi-agent consensus dynamics under delay τ. We report that when the dynamics is unstable under this delay, its states can be naturally bounded, even for arbitrarily large threshold values, preventing agents to disperse indefinitely. This mechanism can also make the system recover stability in a self-regulating manner, mainly induced by network separation and enhanced delay margin. Under certain conditions, unstable consensus dynamics can keep separating into smaller stable subnetwork dynamics until all agents stabilize in their respective subnetworks. Results are then demonstrated on a previously validated robot coordination model, where specifically robustness of τ(*) is studied against the delay τinh inherently present in the orientation measurements of the robots. To this end, a mathematical framework to compute τ(*) with respect to τinh in quasi-state is developed, demonstrating that τ(*) can be sensitive to τinh, yet robot regrouping and stabilization of subnetworks is still possible.
Angular dependence of photoemission time delay in helium
Heuser, Sebastian; Jiménez Galán, Álvaro; Cirelli, Claudio; Marante, Carlos; Sabbar, Mazyar; Boge, Robert; Lucchini, Matteo; Gallmann, Lukas; Ivanov, Igor; Kheifets, Anatoli S.; Dahlström, J. Marcus; Lindroth, Eva; Argenti, Luca; Martín, Fernando; Keller, Ursula
2016-12-01
Time delays of electrons emitted from an isotropic initial state with the absorption of a single photon and leaving behind an isotropic ion are angle independent. Using an interferometric method involving XUV attosecond pulse trains and an IR-probe field in combination with a detection scheme, which allows for full three-dimensional momentum resolution, we show that measured time delays between electrons liberated from the 1 s2 spherically symmetric ground state of helium depend on the emission direction of the electrons relative to the common linear polarization axis of the ionizing XUV light and the IR-probing field. Such time delay anisotropy, for which we measure values as large as 60 as, is caused by the interplay between final quantum states with different symmetry and arises naturally whenever the photoionization process involves the exchange of more than one photon. With the support of accurate theoretical models, the angular dependence of the time delay is attributed to small phase differences that are induced in the laser-driven continuum transitions to the final states. Since most measurement techniques tracing attosecond electron dynamics involve the exchange of at least two photons, this is a general and significant effect that must be taken into account in all measurements of time delays involving photoionization processes.
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.
Stability of the stationary solutions of neural field equations with propagation delays.
Veltz, Romain; Faugeras, Olivier
2011-05-03
In this paper, we consider neural field equations with space-dependent delays. Neural fields are continuous assemblies of mesoscopic models arising when modeling macroscopic parts of the brain. They are modeled by nonlinear integro-differential equations. We rigorously prove, for the first time to our knowledge, sufficient conditions for the stability of their stationary solutions. We use two methods 1) the computation of the eigenvalues of the linear operator defined by the linearized equations and 2) the formulation of the problem as a fixed point problem. The first method involves tools of functional analysis and yields a new estimate of the semigroup of the previous linear operator using the eigenvalues of its infinitesimal generator. It yields a sufficient condition for stability which is independent of the characteristics of the delays. The second method allows us to find new sufficient conditions for the stability of stationary solutions which depend upon the values of the delays. These conditions are very easy to evaluate numerically. We illustrate the conservativeness of the bounds with a comparison with numerical simulation.
Directory of Open Access Journals (Sweden)
Debaldev Jana
2014-01-01
Full Text Available In the present paper, I study a prey-predator model with multiple time delays where the predator population is regarded as generalist. For this regard, I consider a Holling-Tanner prey-predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator. Predator’s interference in predator-prey relationship provides better descriptions of predator's feeding over a range of prey-predator abundances, so the predator's functional response here is considered to be Type II ratio-dependent. In accordance with previous studies, it is observed that delay destabilizes the system, in general, and stability loss occurs via Hopf bifurcation. There exist critical values of delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when delay parameters cross their critical values. When delay parameters are large enough than their critical values, the system exhibits chaotic behavior and this abnormal behavior may be controlled by refuge. Numerical computation is also performed to validate different theoretical results. Lyapunov exponent, recurrence plot, and power spectral density confirm the chaotic dynamical behaviors.
Delay and Its Time-Derivative Dependent Bounded Real Lemma for Linear Time-Delay Systems
Institute of Scientific and Technical Information of China (English)
JIANGXiefu; XUWenli
2004-01-01
Based on an appropriate Lyapunov-Krasovskii functional, this paper deals with the problem of the bounded real lemma for linear continuous-time systems with state delay. The system under consideration involves state time-varying time-delay. A sufficient condition for the system to possess a H∞-norm that is less than a prescribed level, is presented in a Linear matrix inequality(LMI) form which is dependent on both the size of timedelay and the size of its time-derivative. Due to that fewercross terms should be bounded, our result is less conservative. Finally, an example is presented to demonstrate the effectiveness of our result.
Stability of a time discrete perturbed dynamical system with delay
Directory of Open Access Journals (Sweden)
Michael I. Gil'
1999-01-01
Full Text Available Let Cn be the set of n complex vectors endowed with a norm ‖⋅‖Cn. Let A,B be two complex n×n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type uk+1=Auk+Buk−τ+Fk(uk,uk−τ, k=0,1,2,…, where Fk:Cn×Cn→Cn satisfies the condition ‖Fk(x,y‖Cn≤p‖x‖Cn+q‖y‖Cn, k=0,1,2,…, where p and q are positive constants. In this paper, absolute stability conditions for this equation are established.
Modified Schur-Cohn Criterion for Stability of Delayed Systems
Directory of Open Access Journals (Sweden)
Juan Ignacio Mulero-Martínez
2015-01-01
Full Text Available A modified Schur-Cohn criterion for time-delay linear time-invariant systems is derived. The classical Schur-Cohn criterion has two main drawbacks; namely, (i the dimension of the Schur-Cohn matrix generates some round-off errors eventually resulting in a polynomial of s with erroneous coefficients and (ii imaginary roots are very hard to detect when numerical errors creep in. In contrast to the classical Schur-Cohn criterion an alternative approach is proposed in this paper which is based on the application of triangular matrices over a polynomial ring in a similar way as in the Jury test of stability for discrete systems. The advantages of the proposed approach are that it halves the dimension of the polynomial and it only requires seeking real roots, making this modified criterion comparable to the Rekasius substitution criterion.
Zhang, Wei; Huang, Tingwen; He, Xing; Li, Chuandong
2017-11-01
In this study, we investigate the global exponential stability of inertial memristor-based neural networks with impulses and time-varying delays. We construct inertial memristor-based neural networks based on the characteristics of the inertial neural networks and memristor. Impulses with and without delays are considered when modeling the inertial neural networks simultaneously, which are of great practical significance in the current study. Some sufficient conditions are derived under the framework of the Lyapunov stability method, as well as an extended Halanay differential inequality and a new delay impulsive differential inequality, which depend on impulses with and without delays, in order to guarantee the global exponential stability of the inertial memristor-based neural networks. Finally, two numerical examples are provided to illustrate the efficiency of the proposed methods. Copyright © 2017 Elsevier Ltd. All rights reserved.
Absolute stability of nonlinear systems with time delays and applications to neural networks
Directory of Open Access Journals (Sweden)
Xinzhi Liu
2001-01-01
Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
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.
Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems
Directory of Open Access Journals (Sweden)
Hai Zhang
2014-01-01
Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.
Stability and Hopf bifurcation in a delayed competitive web sites model
Energy Technology Data Exchange (ETDEWEB)
Xiao Min [Department of Mathematics, Southeast University, Nanjing 210096 (China): Department of Mathematics, Nanjing Xiaozhuang College, Nanjing 210017 (China); Cao Jinde [Department of Mathematics, Southeast University, Nanjing 210096 (China)]. E-mail: jdcao@seu.edu.cn
2006-04-24
The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found.
Directory of Open Access Journals (Sweden)
Dan Ye
2013-01-01
Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.
Cepeda-Gomez, Rudy; Olgac, Nejat
2016-01-01
We consider a linear algorithm to achieve formation control in a group of agents which are driven by second-order dynamics and affected by two rationally independent delays. One of the delays is in the position and the other in the velocity information channels. These delays are taken as constant and uniform throughout the system. The communication topology is assumed to be directed and fixed. The formation is attained by adding a supplementary control term to the stabilising consensus protocol. In preparation for the formation control logic, we first study the stability of the consensus, using the recent cluster treatment of characteristic roots (CTCR) paradigm. This effort results in a unique depiction of the non-conservative stability boundaries in the domain of the delays. However, CTCR requires the knowledge of the potential stability switching loci exhaustively within this domain. The creation of these loci is done in a new surrogate coordinate system, called the 'spectral delay space (SDS)'. The relative stability is also investigated, which has to do with the speed of reaching consensus. This step leads to a paradoxical control design concept, called the 'delay scheduling', which highlights the fact that the group behaviour may be enhanced by increasing the delays. These steps lead to a control strategy to establish a desired group formation that guarantees spacing among the agents. Example case studies are presented to validate the underlying analytical derivations.
Stability analysis of fractional-order Hopfield neural networks with time delays.
Wang, Hu; Yu, Yongguang; Wen, Guoguang
2014-07-01
This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained 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.
Music-dependent memory in immediate and delayed word recall.
Balch, W R; Bowman, K; Mohler, L
1992-01-01
Undergraduate volunteers rated a series of words for pleasantness while hearing a particular background music. The subjects in Experiment 1 received, immediately or after a 48-h delay, an unexpected word-recall test in one of the following musical cue contexts: same cue (S), different cue (D), or no cue (N). For immediate recall, context dependency (S-D) was significant but same-cue facilitation (S-N) was not. No cue effects at all were found for delayed recall, and there was a significant interaction between cue and retention interval. A similar interaction was also found in Experiment 3, which was designed to rule out an alternative explanation with respect to distraction. When the different musical selection was changed specifically in either tempo or form (genre), only pieces having an altered tempo produced significantly lower immediate recall compared with the same pieces (Experiment 2). The results support a stimulus generalization view of music-dependent memory.
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.
Numerical Investigation of Noise Enhanced Stability Phenomenon in a Time-Delayed Metastable System
Institute of Scientific and Technical Information of China (English)
JIA Zheng-Lin
2008-01-01
@@ The transient properties of a time-delayed metastable system subjected to the additive white noise are investigated by means of the stochastic simulation method. The noise enhanced stability phenomenon (NES) can be observed in this system and the effect of the delay time on the NES shows a critical behaviour, i.e., there is a critical value of the delay time Tc ≈ 1, above which the time delay enhances the NES effect with the delay time increasing and below which the time delay weakens the NES effect as the delay time increases.
Effect of coefficient changes on stability of linear retarded systems with constant time delays
Barker, L. K.
1977-01-01
A method is developed to determine the effect of coefficient changes on the stability of a retarded system with constant time delays. The method, which uses the tau-decomposition method of stability analysis, is demonstrated by an example.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
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.
Directory of Open Access Journals (Sweden)
W. Weera
2011-01-01
theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.
Delay-dependent decentralized H∞ filtering for uncertain interconnected systems
Institute of Scientific and Technical Information of China (English)
Chen Ning; Gui Weihua; Zhang Xiaofeng
2008-01-01
This article considers delay dependent decentralized H∞ filtering for a class of uncertain intercon nected systems,where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions.First,combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices,a sufficient condition of the existence of the robust decentralized H∞ filter is derived,which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties.Then,the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation.Finally,the numerical simulation shows the efficiency of the main results.
GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS
Institute of Scientific and Technical Information of China (English)
张继业
2004-01-01
Without assuming the boundedness and differentiability of the activation functions,the conditions ensuring existence,uniqueness,and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied.Using the idea of vector Liapunov method,the intero-differential inequalities with unbounded delay and variable delays were constructed.By the stability analysis of the intero-differential inequalities,the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.
Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach
Directory of Open Access Journals (Sweden)
Shu-An He
2011-01-01
Full Text Available Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function. This paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the Lambert function. The main issues concerned are the rightmost eigenvalue locations, stability robustness with respect to delay time, and the response performance of the closed-loop system. Examples and simulations are presented to illustrate the analysis results.
Study on Robust Uniform Asymptotical Stability for Uncertain Linear Impulsive Delay Systems
Institute of Scientific and Technical Information of China (English)
刘斌; 刘新芝; 廖晓昕
2003-01-01
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
Exponential stability of Takagi-Sugeno fuzzy systems with impulsive effects and small delays
Institute of Scientific and Technical Information of China (English)
Yu Yong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Bang
2008-01-01
This paper deals with the exponential stability of impulsive Takagi-Sugeno fuzzy systems with delay. Impulsive control and delayed fuzzy control are applied to the system, and the criterion on exponential stability expressed in terms of linear matrix inequalities (LMIs) is presented.
Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay
Directory of Open Access Journals (Sweden)
Yahong Peng
2014-01-01
Full Text Available We consider a model for gene expression with one or two time delays and diffusion. The local stability and delay-induced Hopf bifurcation are investigated. We also derive the formulas determining the direction and the stability of Hopf bifurcations by calculating the normal form on the center manifold.
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.
Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality
Directory of Open Access Journals (Sweden)
Pang Denghao
2014-01-01
Full Text Available This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.
GLOBAL ATTRACTIVITY AND GLOBAL EXPONENTIAL STABILITY FOR DELAYED HOPFIELD NEURAL NETWORK MODELS
Institute of Scientific and Technical Information of China (English)
蒲志林; 徐道义
2001-01-01
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural networks with time delays are presented.
Stability and Hopf Bifurcation of a Predator-Prey Model with Distributed Delays and Competition Term
Directory of Open Access Journals (Sweden)
Lv-Zhou Zheng
2014-01-01
Full Text Available A class of predator-prey system with distributed delays and competition term is considered. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the predator-prey system. According to the theorem of Hopf bifurcation, some sufficient conditions are obtained for the local stability of the positive equilibrium point.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input
Directory of Open Access Journals (Sweden)
Pedro R. Acosta
2013-01-01
Full Text Available This paper deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.
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.
Directory of Open Access Journals (Sweden)
Yang Fang
2016-01-01
Full Text Available The robust exponential stability problem for a class of uncertain impulsive stochastic neural networks of neutral-type with Markovian parameters and mixed time-varying delays is investigated. By constructing a proper exponential-type Lyapunov-Krasovskii functional and employing Jensen integral inequality, free-weight matrix method, some novel delay-dependent stability criteria that ensure the robust exponential stability in mean square of the trivial solution of the considered networks are established in the form of linear matrix inequalities (LMIs. The proposed results do not require the derivatives of discrete and distributed time-varying delays to be 0 or smaller than 1. Moreover, the main contribution of the proposed approach compared with related methods lies in the use of three types of impulses. Finally, two numerical examples are worked out to verify the effectiveness and less conservativeness of our theoretical results over existing literature.
Directory of Open Access Journals (Sweden)
Jun Li
2014-01-01
Full Text Available This paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information on the lower bound of the delay sufficiently, a delay-dependent stability criterion is derived for the proposed UISGRNs model by using the free-weighting matrices method and convex combination technique. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. In addition, three numerical examples are given to justify the obtained stability results.
Energy Technology Data Exchange (ETDEWEB)
Rezaie, B; Motlagh, M R Jahed; Analoui, M [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Khorsandi, S [Amirkabir University of Technology, Hafez St., Tehran (Iran, Islamic Republic of)], E-mail: brezaie@iust.ac.ir
2009-10-02
This paper deals with the problem of Hopf bifurcation control for a class of nonlinear time-delay systems. A dynamic delayed feedback control method is utilized for stabilizing unstable fixed points near Hopf bifurcation. Using a linear stability analysis, we show that under certain conditions of the control parameters, and without changing the operating point of the system, the onset of Hopf bifurcation is delayed. Meanwhile, by applying the center manifold theorem and the normal form theory, we obtain formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions of the closed loop system. Numerical simulations are given to justify the validity of the analytical results for the system controlled by the proposed method.
Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays
Directory of Open Access Journals (Sweden)
Jing Xia
2013-01-01
Full Text Available This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.
Stochastic stability of linear time-delay system with Markovian jumping parameters
Directory of Open Access Journals (Sweden)
K. Benjelloun
1997-01-01
Full Text Available This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP. We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.
Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays
Directory of Open Access Journals (Sweden)
S. Udpin
2013-01-01
Full Text Available This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.
Guesmia, Aissa
2014-08-01
In this paper, we consider a Timoshenko system in one-dimensional bounded domain with infinite memory and distributed time delay both acting on the equation of the rotation angle. Without any restriction on the speeds of wave propagation and under appropriate assumptions on the infinite memory and distributed time delay convolution kernels, we prove, first, the well-posedness and, second, the stability of the system, where we present some decay estimates depending on the equal-speed propagation case and the opposite one. The obtained decay rates depend on the growths of the memory and delay kernels at infinity. In the nonequal-speed case, the decay rate depends also on the regularity of initial data. Our stability results show that the only dissipation resulting from the infinite memory guarantees the asymptotic stability of the system regardless to the speeds of wave propagation and in spite of the presence of a distributed time delay. Applications of our approach to specific coupled Timoshenko-heat and Timoshenko-wave systems as well as the discrete time delay case are also presented.
离散时延双神经元网络的渐近稳定性%Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays
Institute of Scientific and Technical Information of China (English)
李绍文; 李绍荣; 廖晓峰
2003-01-01
New sufficient conditions for the asymptotic stability of a two-neuron network with different time delays are derived. These conditions lead to delay-dependent and delay-independent asymptotic stability. Our results are shown to be less conservative and restrictive than those reported in the literature. Some examples are given to illustrate the correctness of our results.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm bounded parameter perturbetions in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.
Institute of Scientific and Technical Information of China (English)
Xu Rui(徐瑞); Chen Lansun(陈兰荪); M.A.J. Chaplain
2003-01-01
A delayed n-species nonautonomous Lotka-Volterra type competitive systemwithout dominating instantaneous negative feedback is investigated. By means of a suitableLyapunov functional, sufficient conditions are derived for the global asymptotic stability ofthe positive solutions of the system. As a corollary, it is shown that the global asymptoticstability of the positive solution is maintained provided that the delayed negative feedbacksdominate other interspecific interaction effects with delays and the delays are sufficientlysmall.
Liu, Shichao; Liu, Peter Xiaoping; Wang, Xiaoyu
2017-01-01
This survey is to summarize and compare existing and recently emerging approaches for the analysis and compensation of the effects of network-induced delays on the stability and performance of communication-based power control systems. Several important communication-based power control systems are briefly introduced. The deterministic and stochastic methodologies of analyzing the impacts of network-induced delays on the stability of the communication-based power control systems are summarized and compared. A variety of control approaches are reviewed and compared for mitigating the effects of network-induced delays, depending on several design requirements, such as model dependence and design difficulty. The summary and comparison of these control approaches in this survey provide researchers and utilities valuable guidance for designing advanced communication-based power control systems in the future.
Global Stability, Bifurcation, and Chaos Control in a Delayed Neural Network Model
Directory of Open Access Journals (Sweden)
Amitava Kundu
2014-01-01
Full Text Available Conditions for the global asymptotic stability of delayed artificial neural network model of n (≥3 neurons have been derived. For bifurcation analysis with respect to delay we have considered the model with three neurons and used suitable transformation on multiple time delays to reduce it to a system with single delay. Bifurcation analysis is discussed with respect to single delay. Numerical simulations are presented to verify the analytical results. Using numerical simulation, the role of delay and neuronal gain parameter in changing the dynamics of the neural network model has been discussed.
Yu, Jinchen; Peng, Mingshu
2016-10-01
In this paper, a Kaldor-Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.
Exponential stability of cellular neural networks with multiple time delays and impulsive effects
Institute of Scientific and Technical Information of China (English)
Li Dong; Wang Hui; Yang Dan; Zhang Xiao-Hong; Wang Shi-Long
2008-01-01
In this work,the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated.Based on the stability theory of Lyapunov-Krasovskii,the method of linear matrix inequality (LMI) and parametrized first-order model transformation,several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained.A numerical example is given to illustrate the effectiveness of our results.
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.
Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations
Institute of Scientific and Technical Information of China (English)
甘四清; 郑纬民
2004-01-01
Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable Runge-Kutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.
Energy Technology Data Exchange (ETDEWEB)
Waldo, R.W.
1980-05-01
Time-dependent delayed neutron emission is of interest in reactor design, reactor dynamics, and nuclear physics studies. The delayed neutrons from neutron-induced fission of /sup 232/U, /sup 237/Np, /sup 238/Pu, /sup 241/Am, /sup 242m/Am, /sup 245/Cm, and /sup 249/Cf were studied for the first time. The delayed neutron emission from /sup 232/Th, /sup 233/U, /sup 235/U, /sup 238/U, /sup 239/Pu, /sup 241/Pu, and /sup 242/Pu were measured as well. The data were used to develop an empirical expression for the total delayed neutron yield. The expression gives accurate results for a large variety of nuclides from /sup 232/Th to /sup 252/Cf. The data measuring the decay of delayed neutrons with time were used to derive another empirical expression predicting the delayed neutron emission with time. It was found that nuclides with similar mass-to-charge ratios have similar decay patterns. Thus the relative decay pattern of one nuclide can be established by any measured nuclide with a similar mass-to-charge ratio. A simple fission product yield model was developed and applied to delayed neutron precursors. It accurately predicts observed yield and decay characteristics. In conclusion, it is possible to not only estimate the total delayed neutron yield for a given nuclide but the time-dependent nature of the delayed neutrons as well. Reactors utilizing recycled fuel or burning actinides are likely to have inventories of fissioning nuclides that have not been studied until now. The delayed neutrons from these nuclides can now be incorporated so that their influence on the stability and control of reactors can be delineated. 8 figures, 39 tables.
Zhou, Wuneng; Tong, Dongbing; Gao, Yan; Ji, Chuan; Su, Hongye
2012-04-01
In this brief, the analysis problem of the mode and delay-dependent adaptive exponential synchronization in th moment is considered for stochastic delayed neural networks with Markovian switching. By utilizing a new nonnegative function and the -matrix approach, several sufficient conditions to ensure the mode and delay-dependent adaptive exponential synchronization in th moment for stochastic delayed neural networks are derived. Via the adaptive feedback control techniques, some suitable parameters update laws are found. To illustrate the effectiveness of the -matrix-based synchronization conditions derived in this brief, a numerical example is provided finally.
UNITED STABILIZING SCHEME FOR EDGE DELAY IN OPTICAL BURST SWITCHED NETWORKS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A novel scheme, namely united stabilizing scheme for edge delay, is introduced in optical burst switched networks. In the scheme, the limits of burst length and assembly time are both set according to certain qualifications. For executing the scheme, the conception for unit input bit rate is introduced to improve universality, and the assembly algorithm with a buffer safety space under the self-similar traffic model at each ingress edge router is proposed. Then, the components of burst and packet delay are concluded, and the equations that limits of burst length and assembly time should satisfy to stabilize the burst edge delay under different buffer offered loads are educed. The simulation results show that united stabilizing scheme stabilizes both burst and packet edge delay to a great extent when buffer offered load changes from 0.1 to 1, and the edge delay of burst and packet are near the limit values under larger offered load, respectively.
Institute of Scientific and Technical Information of China (English)
RONG LIBIN; LU WENLIAN; CHEN TIANPING
2004-01-01
Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.
Stability and synchronization of memristor-based fractional-order delayed neural networks.
Chen, Liping; Wu, Ranchao; Cao, Jinde; Liu, Jia-Bao
2015-11-01
Global asymptotic stability and synchronization of a class of fractional-order memristor-based delayed neural networks are investigated. For such problems in integer-order systems, Lyapunov-Krasovskii functional is usually constructed, whereas similar method has not been well developed for fractional-order nonlinear delayed systems. By employing a comparison theorem for a class of fractional-order linear systems with time delay, sufficient condition for global asymptotic stability of fractional memristor-based delayed neural networks is derived. Then, based on linear error feedback control, the synchronization criterion for such neural networks is also presented. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
Institute of Scientific and Technical Information of China (English)
Dishen; Jiabu
2006-01-01
This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained.
Robust Stabilization Analysis for Uncertain Systems with Time-Varying Delays
Institute of Scientific and Technical Information of China (English)
WANG Zhong-sheng; WANG Dong-yun; SHEN Yi
2004-01-01
In this paper, the stabilization problem for uncertain systems with time-varying delays both in state and control are discussed. A stabilization criterion is obtained to guarantee the quadratic stability of the closed-loop system. The controller gain matrix is included in an Hamiltonian matrix, which is easily constructed by the boundedness of the uncertainties.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-07-01
In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations.
Directory of Open Access Journals (Sweden)
Hai Zhang
2014-01-01
Full Text Available We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.
Stability of adaptive cruise control systems taking account of vehicle response time and delay
Energy Technology Data Exchange (ETDEWEB)
Davis, L.C., E-mail: ldavis7@mailaps.org [10244 Normandy Dr., Plymouth, MI 48170 (United States)
2012-08-20
The region of string stability of a platoon of adaptive cruise control vehicles, taking into account the delay and response of the vehicle powertrain, is found. An upper bound on the explicit delay time as a function the first-order powertrain response time constant is determined. The system is characterized by a headway time constant, a sensitivity parameter, relative (to the vehicle immediately in front) velocity control, and delayed-velocity feedback or acceleration feedback. -- Highlights: ► I find the region of stability for a realistic adaptive cruise control system. ► Vehicle response time and explicit delay are included in the analysis. ► Delayed-feedback enlarges the parameter space that gives string stability.
Control of Parameter-Dependent Systems, Spatially-Distributed Systems, and Systems with Delays.
1983-12-01
commensurate time delays: Stability and stabilization independent of delay," IEEE Transactions on Automatic Control , Vol. AC-27, pp. 367-375, April 1952. 2...34 IEEE Transactions * on Automatic Control , Vol. AC-29, January 1984 (to appear). I 5. E. W. Kamen, P. P. Khargonekar, and A. Tannenbaum, "Pointwise
Stability and Time Delay Tolerance Analysis Approach for Networked Control Systems
Directory of Open Access Journals (Sweden)
Ashraf F. Khalil
2015-01-01
Full Text Available Networked control system is a research area where the theory is behind practice. Closing the feedback loop through shared network induces time delay and some of the data could be lost. So the network induced time delay and data loss are inevitable in networked control Systems. The time delay may degrade the performance of control systems or even worse lead to system instability. Once the structure of a networked control system is confirmed, it is essential to identify the maximum time delay allowed for maintaining the system stability which, in turn, is also associated with the process of controller design. Some studies reported methods for estimating the maximum time delay allowed for maintaining system stability; however, most of the reported methods are normally overcomplicated for practical applications. A method based on the finite difference approximation is proposed in this paper for estimating the maximum time delay tolerance, which has a simple structure and is easy to apply.
Stability and Hopf bifurcation analysis on Goodwin model with three delays
Energy Technology Data Exchange (ETDEWEB)
Cao Jianzhi [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China); Jiang Haijun, E-mail: jianghai@xju.edu.cn [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)
2011-08-15
Highlights: > Stability and Hopf bifurcation on a delayed Goodwin model are studied. > The sum of the delays is chosen as the bifurcation parameter. > Hopf bifurcation would occur when the delay exceeds a critical value. > A numerical simulation is provided. - Abstract: In this paper, a class of Goodwin models with three delays is dealt. The dynamic properties including stability and Hopf bifurcations are studied. Firstly, we prove analytically that the addressed system possesses a unique positive equilibrium point. Moreover, using the Cardano's formula for the third degree algebra equation, the distribution of characteristic roots is proposed. And then, the sum of the delays is chosen as the bifurcation parameter and it is demonstrated that the Hopf bifurcation would occur when the delay exceeds a critical value. Finally, a numerical simulation for justifying the theoretical results is also provided.
Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays
National Research Council Canada - National Science Library
Ndongo, Abdoul Samba; Talibi Alaoui, Hamad
2014-01-01
.... Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected...
STABILITY CRITERIA FOR A CLASS OF UNCERTAIN SYSTEMS WITH TIME-DELAY
Institute of Scientific and Technical Information of China (English)
Zhongsheng WANG; Zhigang ZENG; Xiaoxin LIAO
2003-01-01
Some stability criteria are obtained for a class of uncertain systems with time-delay using Lyapunov functional and analytic techniques. It is easy to check the criteria by making use of the boundedness of the uncertainties.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, using the theory of topological degree and Liapunov functional methods, the authors study the competitive neural networks with time delays and different time scales and present some criteria of global robust stability for this neural network model.
The influences of delay time on the stability of a market model with stochastic volatility
Li, Jiang-Cheng; Mei, Dong-Cheng
2013-02-01
The effects of the delay time on the stability of a market model are investigated, by using a modified Heston model with a cubic nonlinearity and cross-correlated noise sources. These results indicate that: (i) There is an optimal delay time τo which maximally enhances the stability of the stock price under strong demand elasticity of stock price, and maximally reduces the stability of the stock price under weak demand elasticity of stock price; (ii) The cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time τo. Moreover, the probability density function of the escape time of stock price returns, the probability density function of the returns and the correlation function of the returns are compared with other literatures.
A remark for "Linearization, stability, and oscillation of the discrete delayed logistic system"
Zhang, Binggen
2007-09-01
In this remark, we shall show three counter examples for the main results to the paper [Guanrong Chen, Shu Tang Liu, Linearization, stability, and oscillation of the discrete delayed logistic system, IEEE Trans. Circuits Syst. 50 (2003) 822-826].
Stability analysis and design of amplitude death induced by a time-varying delay connection
Energy Technology Data Exchange (ETDEWEB)
Konishi, Keiji, E-mail: konishi@eis.osakafu-u.ac.j [Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 (Japan); Kokame, Hideki; Hara, Naoyuki [Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 (Japan)
2010-01-18
The present Letter considers amplitude death in a pair of oscillators coupled by a time-varying delay connection. A linear stability analysis is used to derive the boundary curves for amplitude death in a connection parameters space. The delay time can be arbitrarily long for certain amplitude of delay variation and coupling strength. A simple systematic procedure for designing such variation and strength is provided. The theoretical results are verified by a numerical simulation.
Simple stability conditions of linear discrete time systems with multiple delay
Directory of Open Access Journals (Sweden)
Stojanović Sreten B.
2010-01-01
Full Text Available In this paper we have established a new Lyapunov-Krasovskii method for linear discrete time systems with multiple time delay. Based on this method, two sufficient conditions for delay-independent asymptotic stability of the linear discrete time systems with multiple delays are derived in the shape of Lyapunov inequality. Numerical examples are presented to demonstrate the applicability of the present approach.
Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting
Directory of Open Access Journals (Sweden)
Fengying Wei
2014-01-01
Full Text Available A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delay τ passes through critical values. By using of normal form theory and center manifold theorem, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are obtained. Finally, numerical simulations are given to support our theoretical predictions.
Exponential Stabilization of Delay Neutral Systems under Sampled-Data Control
Seuret, Alexandre; Fridman, Emilia; Richard, Jean-Pierre
2005-01-01
International audience; This paper considers the exponential stabilization of delay systems of the neutral type via sampled-data control. The control input of the neutral system can present a delay, constant or variable. The sampling period is not necessarily constant. It is only assumed that the time between to successive sampling instants is bounded. Since the sampling effect (sampling and zero-holder) is equivalent to a variable delay, the resulting system is modelled as a continuous-time ...
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 a noise control system in a duct by using delay differential equation
Institute of Scientific and Technical Information of China (English)
Masakazu Haraguchi; Hai Yan Hu
2009-01-01
The paper deals with the criteria for the closed-loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of acoustic wave governed by a partial differential equation of hyperbolic type. Then, a simple feedback controller is designed, and its closed-loop stability is analyzed on the basis of the derived model of delay differential equation. The obtained criteria reveal the influence of the controller gain and the positions of a sensor and an actuator on the closed-loop stability. Finally, numerical simulations are presented to support the theoreti-cal results.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Directory of Open Access Journals (Sweden)
Hao Chen
2015-01-01
Full Text Available This paper concerns the problem of the globally exponential stability of neural networks with discrete and distributed delays. A novel criterion for the globally exponential stability of neural networks is derived by employing the Lyapunov stability theory, homomorphic mapping theory, and matrix theory. The proposed result improves the previously reported global stability results. Finally, two illustrative numerical examples are given to show the effectiveness of our results.
Method of Time-Delay Calculating and Correcting to Control Spin-Stabilized Satellite Synchronously
Institute of Scientific and Technical Information of China (English)
YangTianshe; LiJisheng; HuangYongxuan
2005-01-01
The key to control Spin-Stabilized Satellites Synchronously is to determine the models for calculating and correcting of time-delay at the different situations. Based on the principle of Synchronous-Control mode, the methods of determining the models of calculating and correcting of time-delay are proposed. The methods have been proved to be effective in real satellite control engineering.
GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS
Institute of Scientific and Technical Information of China (English)
YANG Zhi-chun; XU Dao-yi
2006-01-01
A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.
Energy Technology Data Exchange (ETDEWEB)
Shim, D.S. [Chung-Ang University, Seoul (Korea, Republic of)
1998-04-01
We study the decentralized stabilization problem of linear time-invariant large-scale interconnected systems with delays without any system structure. We obtain sufficient stability conditions for interconnected systems which are equivalent to disturbance attenuation of some scaled system. A decentralized output-feedback controller is obtained using standard H{infinity} control theory. The obtained controller is delay-independent. We also obtain an observer for the interconnected system. (author). 9 refs.
Stability analysis of BAM neural networks with time-varying delays
Institute of Scientific and Technical Information of China (English)
ZHANG Huaguang; WANG Zhanshan
2007-01-01
Some new criteria for the global asymptotic stability of the equilibrium point for the bi-directional associative memory neural networks with time varying delays are presented. The obtained results present the structure of linear matrix inequality which can be solved efficiently. The comparison with some previously reported results in the literature demonstrates that the results in this paper provide one more set of criteria for determining the stability of the bi-directional associative memory neural networks with delays.
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.
STABILITY OF DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, we study the existence and stability of an equilibrium of discrete-time Cohen-Grossberg BAM Neural Networks with delays. We obtain several sufficient conditions ensuring the existence and stability of an equilibrium of such systems, using discrete Halanay-type inequality and vector Lyapunov methods. In addition, we show that the proposed sufficient condition is independent of the delay parameter. An example is given to demonstrate the effectiveness of the results obtained.
Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay
Directory of Open Access Journals (Sweden)
S. J. Sadati
2010-01-01
Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.
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.
Asymptotic stability properties of θ-methods for delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
Stability and oscillations in a slow-fast flexible joint system with transformation delay
Jiang, Shan-Ying; Xu, Jian; Yan, Yao
2014-10-01
Flexible joints are usually used to transfer velocities in robot systems and may lead to delays in motion transformation due to joint flexibility. In this paper, a link-rotor structure connected by a flexible joint or shaft is firstly modeled to be a slow-fast delayed system when moment of inertia of the lightweight link is far less than that of the heavy rotor. To analyze the stability and oscillations of the slow-fast system, the geometric singular perturbation method is extended, with both slow and fast manifolds expressed analytically. The stability of the slow manifold is investigated and critical boundaries are obtained to divide the stable and the unstable regions. To study effects of the transformation delay on the stability and oscillations of the link, two quantitatively different driving forces derived from the negative feedback of the link are considered. The results show that one of these two typical driving forces may drive the link to exhibit a stable state and the other kind of driving force may induce a relaxation oscillation for a very small delay. However, the link loses stability and undergoes regular periodic and bursting oscillation when the transformation delay is large. Basically, a very small delay does not affect the stability of the slow manifold but a large delay affects substantially.
GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS
Institute of Scientific and Technical Information of China (English)
Zhen Jin; Ma Zhien; Han Maoan
2006-01-01
In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.
Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available The stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. In particular, the weak infinitesimal operator of Lyapunov functions in this paper is not required to be negative, which is necessary in the study of the traditional moment stability. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results and demonstrate that time delays in the leakage terms do contribute to the stability of stochastic neural networks.
Li, Zhichen; Bai, Yan; Huang, Congzhi; Cai, Yunfei
2016-03-01
This paper studies the problems of stability analysis and state feedback stabilization for networked control system. By developing a novel delay-partitioning approach, the information on both the range of network-induced delay and the maximum number of consecutive data packet dropouts can be taken into full consideration. Various augmented Lyapunov-Krasovskii functionals (LKFs) with triple-integral terms are constructed for the two delay subintervals. Moreover, the Wirtinger-based inequalities in combination with an improved reciprocal convexity are utilized to estimate the derivatives of LKFs more accurately. The proposed approaches have improved the stability conditions without increasing much computational complexity. Based on the obtained stability criterion, a stabilization controller design approach is also given. Finally, four numerical examples are presented to illustrate the effectiveness and outperformance of the proposed approaches.
Global stability in ecological models with continuous time delays
Energy Technology Data Exchange (ETDEWEB)
Post, W M; Travis, C C
1979-01-01
This model examines the stability properties of a general system of first-order integro-differential equations which describe the dynamics of interacting species populations. A sufficient condition for the global stability of an equilibrium state is derived. This condition is an improvement over the condition derived by Woerz-Busekros (1978) for similar equations in that this condition has intuitive biological interpretations and is verifiable in a finite number of arithmetical steps. This condition is shown to be both necessary and sufficient for global asymptotic stability of the equilibrium for communities of mutualistically interacting species. Application of the results to an ecological system is also provided. (PCS)
Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays
Institute of Scientific and Technical Information of China (English)
Chengming HUANG; Stefan VANDEWALLE
2009-01-01
This paper is concerned with the study of the stability of Runge Kutta-Pouzet methods for Volterra integro-differential equations with delays.We are interested in the comparison between the analytical and numerical stability regions.First,we focus on scalar equations with real coefficients.It is proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution.Then,we consider the multidimensional case.A new stability condition for the stability of the analytical solution is given.Under this condition,the asymptotic stability of Gauss-Pouzet methods is investigated.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
New stability criteria for linear time-delay systems using complete LKF method
Zhang, Ziye; Lin, Chong; Chen, Bing
2015-01-01
This paper focuses on the stability test for linear systems with time-varying delay and provides new stability conditions in terms of linear matrix inequalities (LMIs). The basic idea is the use of complete Lyapunov-Krasovskii functional (LKF) method and the derivation employs the discretisation technique and the reciprocally convex combination. The main feature of this work lies in that the present result not only leads to some improvements over existing results in the LMI framework but also is applicable for time-delay systems with unstable delay-free case. Three numerical examples are given to show the effectiveness and merits of the present result.
ORIGINAL ARTICLE Stability Analysis of Delayed Cournot Model in ...
African Journals Online (AJOL)
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.
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,a class of bidirectional associative memory(BAM) recurrent neural networks with delays are studied.By a fixed point theorem and a Lyapunov functional,some new sufficient conditions for the existence,uniqueness and global exponential stability of the almost periodic solutions are established.These conditions are easy to be verified and our results complement the previous known results.
Stimulus-dependent synchronization in delayed-coupled neuronal networks.
Esfahani, Zahra G; Gollo, Leonardo L; Valizadeh, Alireza
2016-03-22
Time delay is a general feature of all interactions. Although the effects of delayed interaction are often neglected when the intrinsic dynamics is much slower than the coupling delay, they can be crucial otherwise. We show that delayed coupled neuronal networks support transitions between synchronous and asynchronous states when the level of input to the network changes. The level of input determines the oscillation period of neurons and hence whether time-delayed connections are synchronizing or desynchronizing. We find that synchronizing connections lead to synchronous dynamics, whereas desynchronizing connections lead to out-of-phase oscillations in network motifs and to frustrated states with asynchronous dynamics in large networks. Since the impact of a neuronal network to downstream neurons increases when spikes are synchronous, networks with delayed connections can serve as gatekeeper layers mediating the firing transfer to other regions. This mechanism can regulate the opening and closing of communicating channels between cortical layers on demand.
Asymptotic Stability of Neutral Differential Equations with Unbounded Delay
Institute of Scientific and Technical Information of China (English)
YE Hai-ping; GAO Guo-zhu
2002-01-01
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt [x(t)- P(t)x(h(t))] + Q(t)x(q(t)) -R(t)x(r(t))= 0, t ≥ t0,where P(t)∈ C([t0, ∞), R), Q(t), R(t) ∈ C([t0,∞ ), R+ ), and h, q, r: [ t0, ∞ ) → R are continuously differentiable and strictly increasing, h( t) ＜ t, q( t) ＜t, r(t) ＜ t for all t ≥ t0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable.
The global stability of a delayed predator-prey system with two stage-structure
Energy Technology Data Exchange (ETDEWEB)
Wang Fengyan [College of Science, Jimei University, Xiamen Fujian 361021 (China)], E-mail: wangfy68@163.com; Pang Guoping [Department of Mathematics and Computer Science, Yulin Normal University, Yulin Guangxi 537000 (China)
2009-04-30
Based on the classical delayed stage-structured model and Lotka-Volterra predator-prey model, we introduce and study a delayed predator-prey system, where prey and predator have two stages, an immature stage and a mature stage. The time delays are the time lengths between the immature's birth and maturity of prey and predator species. Results on global asymptotic stability of nonnegative equilibria of the delay system are given, which generalize and suggest that good continuity exists between the predator-prey system and its corresponding stage-structured system.
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.
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.
Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays
Directory of Open Access Journals (Sweden)
Chang-Wen Zhao
2008-07-01
Full Text Available We consider the mean square asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are also given to illustrate our results.
STABILITY AND BIFURCATION OF A HUMAN RESPIRATORY SYSTEM MODEL WITH TIME DELAY
Institute of Scientific and Technical Information of China (English)
沈启宏; 魏俊杰
2004-01-01
The stability and bifurcation of the trivial solution in the two-dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem. Furthermore, numerical simulation was carried out.
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
Energy Technology Data Exchange (ETDEWEB)
Song Yongli E-mail: songyl@sjtu.edu.cn; Han Maoan; Peng Yahong
2004-12-01
We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
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.
Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay
Chunodkar, Apurva A.; Akella, Maruthi R.
2013-12-01
This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.
H∞control for uncertain Markovian jump systems with mode-dependent mixed delays
Institute of Scientific and Technical Information of China (English)
Yingchun Wang; Huaguang Zhang
2008-01-01
We study the problem of H∞ control for a class of Markovian jump systems with norm-bounded parameter uncertainties and mode-dependent mixed delays including discrete delays and distributed delays in this paper. Our aim is to present a new delay-dependent control approach such that the resulting closed-loop system is robust mean-square (MS) exponentially stable and satisfies a prescribed H∞ performance level, irrespective of the parameter uncertainties. Such delay-dependent approach does not require system transformation or free-weighting matrix. A numerical example shows that the results are less conservative and more effective.
Stability on time-dependent domains: convective and dilution effects
Krechetnikov, R.; Knobloch, E.
2017-03-01
We explore near-critical behavior of spatially extended systems on time-dependent spatial domains with convective and dilution effects due to domain flow. As a paradigm, we use the Swift-Hohenberg equation, which is the simplest nonlinear model with a non-zero critical wavenumber, to study dynamic pattern formation on time-dependent domains. A universal amplitude equation governing weakly nonlinear evolution of patterns on time-dependent domains is derived and proves to be a generalization of the standard Ginzburg-Landau equation. Its key solutions identified here demonstrate a substantial variety-spatially periodic states with a time-dependent wavenumber, steady spatially non-periodic states, and pulse-train solutions-in contrast to extended systems on time-fixed domains. The effects of domain flow, such as bifurcation delay due to domain growth and destabilization due to oscillatory domain flow, on the Eckhaus instability responsible for phase slips in spatially periodic states are analyzed with the help of both local and global stability analyses. A nonlinear phase equation describing the approach to a phase-slip event is derived. Detailed analysis of a phase slip using multiple time scale methods demonstrates different mechanisms governing the wavelength changing process at different stages.
Institute of Scientific and Technical Information of China (English)
丛玉豪
2001-01-01
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations. After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGPG-stable if and only if it is A-stable.
Directory of Open Access Journals (Sweden)
Chuangxia Huang
2011-01-01
Full Text Available Stability of reaction-diffusion recurrent neural networks (RNNs with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
Stability with respect to initial time difference for generalized delay differential equations
Directory of Open Access Journals (Sweden)
Ravi Agarwal
2015-02-01
Full Text Available Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability with initial time difference are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations are employed. Several examples are given to illustrate the theory.
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.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Local Stability of AIDS Epidemic Model Through Treatment and Vertical Transmission with Time Delay
Novi W, Cascarilla; Lestari, Dwi
2016-02-01
This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.
Aging-dependent reduction in glyoxalase 1 delays wound healing.
Fleming, Thomas H; Theilen, Till-Martin; Masania, Jinit; Wunderle, Marius; Karimi, Jamshid; Vittas, Spiros; Bernauer, Rainer; Bierhaus, Angelika; Rabbani, Naila; Thornalley, Paul J; Kroll, Jens; Tyedmers, Jens; Nawrotzki, Ralph; Herzig, Stephan; Brownlee, Michael; Nawroth, Peter P
2013-01-01
Methylglyoxal (MG), the major dicarbonyl substrate of the enzyme glyoxalase 1 (GLO1), is a reactive metabolite formed via glycolytic flux. Decreased GLO1 activity in situ has been shown to result in an accumulation of MG and increased formation of advanced glycation endproducts, both of which can accumulate during physiological aging and at an accelerated rate in diabetes and other chronic degenerative diseases. To determine the physiological consequences which result from elevated MG levels and the role of MG and GLO1 in aging, wound healing in young (≤12 weeks) and old (≥52 weeks) wild-type mice was studied. Old mice were found to have a significantly slower rate of wound healing compared to young mice (74.9 ± 2.2 vs. 55.4 ± 1.5% wound closure at day 6; 26% decrease; p wounds of young mice, decreased wound healing by 24% compared to untreated mice, whereas application of BSA modified minimally by MG had no effect. Treatment of either young or old mice with aminoguanidine, a scavenger of free MG, significantly increased wound closure by 16% (66.8 ± 1.6 vs. 77.2 ± 3.1%; p wound healing in the old mice was restored to the level observed in the young mice. These findings were confirmed in vitro, as MG reduced migration and proliferation of fibroblasts derived from young and old, wild-type mice. The data demonstrate that the balance between MG and age-dependent GLO1 downregulation contributes to delayed wound healing in old mice. Copyright © 2013 S. Karger AG, Basel.
Wavelength dependent delay in the onset of FEL tissue ablation
Energy Technology Data Exchange (ETDEWEB)
Tribble, J.A.; Edwards, G.S. [Vanderbilt Univ., Nashville, TN (United States); Lamb, J.A. [Massachusetts General Hospital, Boston, MA (United States)] [and others
1995-12-31
We are investigating the wavelength dependence of the onset of laser tissue ablation in the IR Visible and UV ranges. Toward this end, we have made simultaneous measurements of the ejected material (using a HeNe probe beam tangential to the front surface) and the residual stress transient in the tissue (using traditional piezoelectric detection behind the thin samples). For the IR studies we have used the Vanderbilt FEL and for the UV and Vis range we have used a Q-switched ND:Yag with frequency doubling and quadrupling. To satisfy the conditions of the near field limit for the detection of the stress transient, the duration of the IR FEL macropulse must be as short as possible. We have obtained macropulses as short as 100 ns using Pockels Cell technology. The recording of the signals from both the photodiode monitoring the HeNe probe beam and the acoustic detector are synchronized with the arrival of the 100 ns macropulse. With subablative intensities, the resulting stress transient is bipolar with its positive peak separated from its negative peak by 100 ns in agreement with theory. Of particular interest is the comparison of ablative results using 3 {mu}m and 6.45 {mu}m pulses. Both the stress transient and the ejection of material suffer a greater delay (with respect to the arrival of the 100 ns pulse) when the FEL is tuned to 3 {mu}m as compared to 6.45 {mu}m. A comparison of IR Vis and UV data will be discussed in terms of microscopic mechanisms governing the laser ablation process.
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.
Stability Analysis of Networked Control Systems With Aperiodic Sampling and Time-Varying Delay.
Chen, Jie; Meng, Su; Sun, Jian
2016-12-01
This paper addresses the stability of networked control systems with aperiodic sampling and time-varying network-induced delay. The sampling intervals are assumed to vary within a known interval. The transmission delay is assumed to belong to a given interval. The closed-loop system is first converted to a discrete-time system with multiple time-varying delays and norm-bounded uncertainties resulting from the variation of the sampling intervals. And then, it is transformed into a delay-free system being form of an interconnection of two subsystems. By utilizing scaled small gain theorem, an asymptotic stability criterion for the closed-loop system is proposed in terms of linear matrix inequality. Finally, numerical examples demonstrate the effectiveness of the proposed method and its advantages over existing methods.
Computation of stabilizing PI and PID controllers for processes with time delay.
Tan, Nusret
2005-04-01
In this paper, a new method for the computation of all stabilizing PI controllers for processes with time delay is given. The proposed method is based on plotting the stability boundary locus in the (kp, ki) plane and then computing the stabilizing values of the parameters of a PI controller for a given time delay system. The technique presented does not need to use Pade approximation and does not require sweeping over the parameters and also does not use linear programming to solve a set of inequalities. Thus it offers several important advantages over existing results obtained in this direction. Beyond stabilization, the method is used to compute stabilizing PI controllers which achieve user specified gain and phase margins. The proposed method is also used to design PID controllers for control systems with time delay. The limiting values of a PID controller which stabilize a given system with time delay are obtained in the (kp, ki) plane, (kp, kd) plane, and (ki, kd) plane. Examples are given to show the benefits of the method presented.
Institute of Scientific and Technical Information of China (English)
XIAO Shen-ping; WU Min; SHE Jin-hua
2008-01-01
The problem of designing a non-fragile delay-dependent H∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral inequality method and Lyapunov-Krasovskii stability theory were used to derive new delay-dependent bounded real lemmas for a non-fragile state-feedback controller containing additive or multiplicative uncertainties. They ensure that the closed-loop system is internally stable and has a given H∞ disturbance attenuation level. Then, methods of designing a non-fragile H∞ state feedback controller were presented. No parameters need to be tuned and can be easily determined by solving linear matrix inequalities. Finally, the validity of the proposed methods was demonstrated by a numerical example with the asymptotically stable curves of system state and controller output under the initial condition of x(0)=[1 0 -1]T and h=0.8 time-delay boundary.
Institute of Scientific and Technical Information of China (English)
Peng CUI; Chenghui ZHANG
2008-01-01
The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed.The sufficient conditions of the existence of observers,which are normal linear time-delay systems,and the corresponding design steps are presented via linear matrix inequality(LMI).Moreover,the observer-based feedback stabilizing controller is obtained.Three examples are given to show the effectiveness of the proposed methods.
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.
Global exponential stability of Cohen-Grossberg neural networks with variable delays
Institute of Scientific and Technical Information of China (English)
ZHANG Li-juan; SHI Bao
2009-01-01
A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable delays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions are derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.
Institute of Scientific and Technical Information of China (English)
Dongfang Lv; Shen Cong
2015-01-01
The paper is concerned with stabilization problem for a class of stochastic switching systems with time⁃delay in the detection of switching signal. By using binomial model, Poisson process, and Wiener process to describe time⁃delay, switching signal, and exogenous disturbance, respectively, the system under investigation is entirely set in a stochastic framework. The influence of the random time⁃delay is combined into reconstructing the switching signal of overall closed⁃loop system and changes the distribution property of switching points. Therefore, based on the asymptotical behaviors of Poisson processes and Wiener processes, the almost surely exponential stability conditions are established. Furthermore, a design methodology is posed for solving the stabilization control.
Li, Zhichen; Bai, Yan; Huang, Congzhi; Yan, Huaicheng
2017-05-01
This paper investigates the stability and stabilization problems for interval time-delay systems. By introducing a new delay partitioning approach, various Lyapunov-Krasovskii functionals with triple-integral terms are established to make full use of system information. In order to reduce the conservatism, improved integral inequalities are developed for estimation of double integrals, which show remarkable outperformance over the Jensen and Wirtinger ones. Particularly, the relationship between the time-delay and each subinterval is taken into consideration. The resulting stability criteria are less conservative than some recent methods. Based on the derived condition, the state-feedback controller design approach is also given. Finally, the numerical examples and the application to inverted pendulum system are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Stability for delayed generalized 2D discrete logistic systems
Directory of Open Access Journals (Sweden)
Guanrong Chen
2004-12-01
Full Text Available This paper is concerned with delayed generalized 2D discrete logistic systems of the form xm+1,n=f(m,n,xm,n,xm,n+1,xmÃ¢ÂˆÂ’ÃÂƒ,nÃ¢ÂˆÂ’ÃÂ„ , where ÃÂƒ and ÃÂ„ are positive integers, f:Ã¢Â„Â•02ÃƒÂ—Ã¢Â„Â3Ã¢Â†Â’Ã¢Â„Â is a real function, which contains the logistic map as a special case, and m and n are nonnegative integers, where Ã¢Â„Â•0={0,1,Ã¢Â€Â¦} and Ã¢Â„Â=(Ã¢ÂˆÂ’Ã¢ÂˆÂž,Ã¢ÂˆÂž. Some sufficient conditions for this system to be stable and exponentially stable are derived.
Local Bifurcations Analysis of a State-Dependent Delay Diﬀerential Equation
Directory of Open Access Journals (Sweden)
V. O. Golubenets
2015-01-01
Full Text Available In this paper, a ﬁrst-order equation with state-dependent delay and with a nonlinear right-hand side is considered. Conditions of existence and uniqueness of the solution of initial value problem aresupposed to be executed. The task is to study the behavior of solutions of the considered equation in a small neighborhood of its zero equilibrium. Local dynamics depends on real parameters which are coeﬃcients of equation right-hand side decomposition in a Taylor series. The parameter which is a coeﬃcient at the linear part of this decomposition has two critical values which determine a stability domain of zero equilibrium. We introduce a small positive parameter and use the asymtotic method of normal forms in order to investigate local dynamics modiﬁcations of the equation near each two critical values. We show that the stability exchange bifurcation occurs in the considered equation near the ﬁrst of these critical values, and the supercritical Andronov – Hopf bifurcation occurs near the second of them (if the suﬃcient condition is executed. Asymptotic decompositions according to correspondent small parameters are obtained for each stable solution. Next, a logistic equation with state-dependent delay is considered as an example. The bifurcation parameter of this equation has one critical value. A simple suﬃcient condition of Andronov – Hopf bifurcation occurence in the considered equation near a critical value is obtained as a result of applying the method of normal forms.
Controllability and stability of primary frequency control from thermostatic loads with delays
DEFF Research Database (Denmark)
Ziras, Charalampos; Vrettos, Evangelos; You, Shi
2017-01-01
There is an increasing interest in exploiting the flexibility of loads to provide ancillary services to the grid. In this paper we study how response delays and lockout constraints affect the controllability of an aggregation of refrigerators offering primary frequency control (PFC). First we...... examine the effect of delays in PFC provision from an aggregation of refrigerators, using a two-area power system. We propose a framework to systematically address frequency measurement and response delays and we determine safe values for the total delays via simulations. We introduce a controllability...... index to evaluate PFC provision under lockout constraints of refrigerators compressors. We conduct extensive simulations to study the effects of measurement delay, ramping times, lockout durations and rotational inertia on the controllability of the aggregation and system stability. Finally, we discuss...
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
Xu, Changjin; Li, Peiluan; Pang, Yicheng
2016-12-01
In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence
Directory of Open Access Journals (Sweden)
Shuxue Mao
2011-01-01
Full Text Available We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delay τ passes through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.
Stability, bifurcation and a new chaos in the logistic differential equation with delay
Jiang, Minghui; Shen, Yi; Jian, Jigui; Liao, Xiaoxin
2006-02-01
This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation.
Stabilization of a scalar equation with delay in the state and control variables
SHAYAKHMETOVA LILIYA VLADIMIROVNA; KHARITONOV VLADIMIR LEONIDOVICH
2014-01-01
The contribution is dedicated to the stabilization problem of systems with input and state delay. We derive a stabilizing control law for the case of a scalar equation with several state and two input delays. We start with a control law of the form, where the right hand side contains future values of the state predicted by Cauchy formula. The presented control law is of the form of an integral equation. It is shown that the characteristic function of the closed-loop system consists of two fac...
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Institute of Scientific and Technical Information of China (English)
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
Phased-Array Antenna Beam Squinting Related to Frequency Dependency of Delay Circuits
Garakoui, S.K.; Klumperink, E.A.M.; Nauta, B.; Vliet, F.E. van
2011-01-01
Practical time delay circuits do not have a perfectly linear phase-frequency characteristic. When these delay circuits are applied in a phased-array system, this frequency dependency shows up as a frequency dependent beam direction (“beam squinting”). This paper quantifies beam squinting for a linea
Stability on FInite Time Interval and Time—Dependent Bifurcation Analysis of Duffing‘s Equations6
Institute of Scientific and Technical Information of China (English)
CuncaiHUA; QishaoLU
1999-01-01
The concept of stability on finite time interval is proposed and some stability theorems are established.The delayed bifurcation transition of Duffing's equations with a time-dependent parameter is analyzed.Function is used to predict the bifurcation transition value.The sensitivity of the solutions to initial values and parameters is also studied.
Directory of Open Access Journals (Sweden)
Vu Ngoc Phat
2008-02-01
Full Text Available This paper addresses the problem of exponential stability for a class of uncertain linear non-autonomous time-delay systems. Here, the parameter uncertainties are time-varying and unknown but norm-bounded and the delays are time-varying. Based on combination of the Riccati equation approach and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust stability are obtained in terms of the solution of Riccati-type equations. The approach allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. As an application, sufficient conditions for the robust stabilization are derived. Numerical examples illustrated the results are given.
Stability Analysis of a Predecessor-Following Platoon of Vehicles With Two Time Delays
Directory of Open Access Journals (Sweden)
Ali Ghasemi
2015-03-01
Full Text Available The problem of controlling a platoon of vehicles moving in one dimension is considered so that they all follow a lead vehicle with constant spacing between successive vehicles. The stability and the string stability of a platoon of vehicles with two independent and uncertain delays, one in the inter-vehicle distance and the other in the relative velocity information channels, are considered. The main objectives of this paper are: (1 using a simplifying factorization procedure and deploying the cluster treatment of characteristic roots (CTCR paradigm to obtain exact stability boundaries in the domain of the delays, and (2 for the purpose of disturbance attenuation, the string stability analysis is examined. Finally, a simulation example of multiple vehicle platoon control is used to demonstrate the effectiveness of the proposed method.
Thermal Aware Floorplanning Incorporating Temperature Dependent Wire Delay Estimation
DEFF Research Database (Denmark)
Winther, AndreasThor; Liu, Wei; Nannarelli, Alberto
2015-01-01
Temperature has a negative impact on metal resistance and thus wire delay. In state-of-the-art VLSI circuits, large thermal gradients usually exist due to the uneven distribution of heat sources. The difference in wire temperature can lead to performance mismatch because wires of the same length ...
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
Robust stabilization using LMI techniques of neutral time-delay systems subject to input saturation
El Fezazi, Nabil; El Haoussi, Fatima; Houssaine Tissir, El; Alvarez, Teresa; Tadeo, Fernando
2017-01-01
The robust stabilization of uncertain saturated neutral systems with state delay is solved in this paper: based on a free weighting matrix approach, sufficient conditions are obtained via an LMI formulation. From these conditions, state feedback gains that ensure stability for the largest set of admissible initial conditions can be calculated solving optimization problems with LMI constraints. Some applications of this methodology to feedback control are then presented and compared with previous results in the literature.
Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach
Radek Matušů; Roman Prokop
2015-01-01
The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic qua...
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.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator
Directory of Open Access Journals (Sweden)
Xiao Zhang
2009-01-01
Full Text Available A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.
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.
Institute of Scientific and Technical Information of China (English)
VANGQUANYI
1997-01-01
This paper deals with the problems on the existence and uniqueness and stability of almostperiodic solutions for functional differential equations with infinite delays. The author obtainssome sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment. The results extend all the results of the paper[1] and solve the two open problems proposed in [1] under much weaker conditions than that proposed in [1].
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
A new result on global exponential robust stability of neural networks with time-varying delays
Institute of Scientific and Technical Information of China (English)
Jinliang SHAO; Tingzhu HUANG
2009-01-01
In this paper,the global exponential robust stability of neural networks with time-varying delays is investigated.By using nonnegative matrix theory and the Halanay inequality,a new sufficient condition for global exponential robust stability is presented.It is shown that the obtained result is different from or improves some existing ones reported in the literatures.Finally,some numerical examples and a simulation are given to show the effectiveness of the obtained result.
Analytic curve frequency-sweeping stability tests for systems with commensurate delays
Li, Xu-Guang; Cela, Arben
2015-01-01
In this brief the authors establish a new frequency-sweeping framework to solve the complete stability problem for time-delay systems with commensurate delays. The text describes an analytic curve perspective which allows a deeper understanding of spectral properties focusing on the asymptotic behavior of the characteristic roots located on the imaginary axis as well as on properties invariant with respect to the delay parameters. This asymptotic behavior is shown to be related by another novel concept, the dual Puiseux series which helps make frequency-sweeping curves useful in the study of general time-delay systems. The comparison of Puiseux and dual Puiseux series leads to three important results: an explicit function of the number of unstable roots simplifying analysis and design of time-delay systems so that to some degree they may be dealt with as finite-dimensional systems; categorization of all time-delay systems into three types according to their ultimate stability properties; and a simple frequenc...
An improved robust stability result for uncertain neural networks with multiple time delays.
Arik, Sabri
2014-06-01
This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay.The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results.The key step in the method was to construct a special type of Lyapunov functional for the filter design problem.Unlike the existing techniques,the proposed method employed neither free weighting matrices nor any model transformation,le...
Zhong, Qishui; Cheng, Jun; Zhao, Yuqing
2015-07-01
In this paper, a novel method is developed for delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays. New sufficient condition for stochastic boundness of Markovian jumping neural networks is presented and proved by an newly augmented stochastic Lyapunov-Krasovskii functional and novel activation function conditions, the state trajectory remains in a bounded region of the state space over a given finite-time interval. Finally, a numerical example is given to illustrate the efficiency and less conservative of the proposed method.
Stabilization of the Wave Equation with Boundary Time-Varying Delay
Directory of Open Access Journals (Sweden)
Hao Li
2014-01-01
Full Text Available We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.
Explicit Conditions for Stability of Nonlinear Scalar Delay Impulsive Difference Equation
Directory of Open Access Journals (Sweden)
Bo Zheng
2010-01-01
Full Text Available Sufficient conditions are obtained for the uniform stability and global attractivity of the zero solution of nonlinear scalar delay impulsive difference equation, which extend and improve the known results in the literature. An example is also worked out to verify that the global attractivity condition is a sharp condition.
Stability and Hopf Bifurcation for Two Advertising Systems, Coupled with Delay
Sterpu, Mihaela; Rocşoreanu, Carmen
2007-09-01
Two advertising systems were linearly coupled via the first variable, with time delay. The stability and the Hopf bifurcation corresponding to the symmetric equilibrium point (the origin) in the 4D system are analyzed. Different types of oscillations corresponding to the limit cycles are compared.
PERMANENCE AND GLOBAL STABILITY OF A FEEDBACK CONTROL SYSTEM WITH DELAYS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.
Minimal data rate stabilization of nonlinear systems over networks with large delays
Persis, Claudio De
2007-01-01
We consider the problem of designing encoders, decoders and controllers which stabilize feedforward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilizatioln of the
Institute of Scientific and Technical Information of China (English)
ZHU Qing; LIANG Fang; ZHANG Qing
2009-01-01
In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.
Stability of Delayed Hopfield Neural Networks with Variable-Time Impulses
Directory of Open Access Journals (Sweden)
Yangjun Pei
2014-01-01
Full Text Available In this paper the globally exponential stability criteria of delayed Hopfield neural networks with variable-time impulses are established. The proposed criteria can also be applied in Hopfield neural networks with fixed-time impulses. A numerical example is presented to illustrate the effectiveness of our theoretical results.
Existence and Stability for Stochastic Partial Differential Equations with Infinite Delay
Directory of Open Access Journals (Sweden)
Jing Cui
2014-01-01
Full Text Available We consider a class of neutral stochastic partial differential equations with infinite delay in real separable Hilbert spaces. We derive the existence and uniqueness of mild solutions under some local Carathéodory-type conditions and also exponential stability in mean square of mild solutions as well as its sample paths. Some known results are generalized and improved.
A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
WANG Zhong-sheng; WANG Dong-yun; LIAO Xiao-xin
2005-01-01
The robust stabilization problem for uncertain systems with time-varying delay has been discussed. A new sufficient criterion is obtained to guarantee the closed-loop system robust stabilizable. The controller gain matrix is included in a Hamiltonian matrix. The Hamiltonian matrix can be constructed by the boundedness of the uncertainties. Some examples are given to illustrate the feasibility of the criterion.
Exponential Stability Analysis of Cohen-Grossberg Neural Networks with Time-varying Delays
Institute of Scientific and Technical Information of China (English)
Yi-min MENG; Li-hong HUANG; Zhao-hui YUAN
2012-01-01
In this paper,we study Cohen-Grossberg neural networks (CGNN) with time-varying delay.Based on Halanay inequality and continuation theorem of the coincidence degree,we obtain some sufficient conditions ensuring the existence,uniqueness,and global exponential stability of periodic solution.Our results complement previously known results.
Chen, Guiling
2013-01-01
This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Global exponential stability analysis of cellular neural networks with multiple time delays
Institute of Scientific and Technical Information of China (English)
Zhanshan WANG; Huaguang ZHANG
2007-01-01
Global exponential stability problems are investigated for cellular neural networks (CNN) with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.
Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay
Directory of Open Access Journals (Sweden)
Ruiqing Shi
2013-01-01
Full Text Available We propose a two-dimensional predatory-prey model with discrete and distributed delay. By the use of a new variable, the original two-dimensional system transforms into an equivalent three-dimensional system. Firstly, we study the existence and local stability of equilibria of the new system. And, by choosing the time delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the time delay τ passes through some critical values. Secondly, by the use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, an example with numerical simulations is provided to verify the theoretical results. In addition, some simple discussion is also presented.
Directory of Open Access Journals (Sweden)
D. RAMA REDDY
2012-07-01
Full Text Available This paper describes the stability regions of PID (Proportional +Integral+ Derivative and a new PID with series leading correction (SLC for Networked control system with time delay. The new PID controller has a tuning parameter ‘β’. The relation between β, KP, KI and KD is derived. The effect of plant parameters on stabilityregion of PID controllers and SLC-PID controllers in first-order and second-order systems with time delay are also studied. Finally, an open-loop zero was inserted into the plant-unstable second order system with time delay so that the stability regions of PID and SLC-PID controllers get effectively enlarged. The total system isimplemented using MATLAB/Simulink.
Stability and delay in a three species predator-prey system
Kundu, Soumen; Maitra, Sarit
2016-06-01
In this article a multi-team delayed predator-prey model has been considered. There are two preys and one predator species in this model and the time delay appears for gestation of the predator. The essential mathematical features of the proposed model around the interior equilibrium point are studied in terms of local asymptotic stability by constructing a suitable Lyapunov functional and the condition for existence of Hopf-bifurcation is derived. By the assumption that the prey teams may help each other the effect of the rate of cooperation on the stability of the predator-prey model has been observed. Numerically a critical value for the delay parameter is obtained as a condition for Hopf-bifurcation.
Bending behavior of double-row stabilizing piles with constructional time delay
Institute of Scientific and Technical Information of China (English)
Yang YU; Yue-quan SHANG; Hong-yue SUN
2012-01-01
The bending behavior of double-row stabilizing plies is associated with the constructional time delay (CTD),which can be defined as the time interval between the installations of the front stabilizing pile and the rear stabilizing pile.This paper investigates the effect of CTD on the bending moments of double-row stabilizing piles and a method for determining the optimal CTD is proposed.The stabilizing pile is modeled as a cantilever pile embedded in the Winkler elastic foundation.A triangular distributed earth pressure is assumed on the pile segment in the sliding layer.The front stabilizing pile and the rear stabilizing pile are connected by a beam with pinned joints.The analytical solutions of bending moments on the front and the rear stabilizing piles are derived and the accuracy of bending moment solutions is validated by comparing the tensile strain measured from the Hongyan landslide project,Taizhou,Zhejiang,China.It is concluded that CTD has a significant influence on the bending moments of double-row stabilizing piles.An optimal CTD can be obtained when the maximum tensile stress in the front stabilizing pile is equal to that in the rear stabilizing pile,which is 1.4 months for the Hongyan landslide project.
Directory of Open Access Journals (Sweden)
Chen Qin
2013-01-01
Full Text Available This paper considers the problems of the robust stability and robust H∞ controller design for time-varying delay switched systems using delta operator approach. Based on the average dwell time approach and delta operator theory, a sufficient condition of the robust exponential stability is presented by choosing an appropriate Lyapunov-Krasovskii functional candidate. Then, a state feedback controller is designed such that the resulting closed-loop system is exponentially stable with a guaranteed H∞ performance. The obtained results are formulated in the form of linear matrix inequalities (LMIs. Finally, a numerical example is provided to explicitly illustrate the feasibility and effectiveness of the proposed method.
Robust stabilizing first-order controllers for a class of time delay systems.
Saadaoui, Karim; Testouri, Sana; Benrejeb, Mohamed
2010-07-01
In this paper, stabilizing regions of a first-order controller for an all poles system with time delay are computed via parametric methods. First, the admissible ranges of one of the controller's parameters are obtained. Then, for a fixed value of this parameter, stabilizing regions in the remaining two parameters are determined using the D-decomposition method. Phase and gain margin specifications are then included in the design. Finally, robust stabilizing first-order controllers are determined for uncertain plants with an interval type uncertainty in the coefficients. Examples are given to illustrate the effectiveness of the proposed method.
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.
Stochastic stability of networked control systems with network-induced delay and data dropout
Institute of Scientific and Technical Information of China (English)
Xiaomei ZHANG; Yufan ZHENG; Guoping LU
2008-01-01
This paper deals with the stochastic stability of networked control systems with the presence of networkinduced delay and transmitted data dropout.Based on the Lyapunov approach.safficient conditions for the mean-square stability of the networked control system are derived subiect that the sequence of transmission interval is driven by an identicaily independently distributed sequence and by a finite state Markov chain.respectively.Stabilization controllers are constructed in tcrims of linear matrix inequalities correspondingly.An example is provided to illustrate our results.
Institute of Scientific and Technical Information of China (English)
祝乔; 胡广大
2009-01-01
This paper deals with the robust stability of a class of uncertain nonlinear time-delay systems. A quasi-one-sided Lipschitz condition is introduced to estimate the in-fluenee of nonlinear vector function on the stability analy-sis. Delay-independent/delay-dependent stability criteria for-mulated in the form of linear matrix inequalities are pre-sented. Furthermore, these stability criteria are available even if the system parameter is unstable, because the unneces-sary positive quasi-one-sided Lipschitz constant matrix includes much useful information of the nonlinear part. Numerical ex-amplee show the advantage of the results obtained in this paper.
Vyhlídal, Tomáš; Olgac, Nejat; Kučera, Vladimír
2014-12-01
This paper deals with the problem of active vibration suppression using the concept of delayed resonator (DR) absorber with acceleration feedback. A complete dynamic analysis of DR and its coupling with a single degree of freedom mechanical system are performed. Due to the presence of a delay in the acceleration feedback, the dynamics of the resonator itself, as well as the dynamics of combined system are of ‘neutral' character. On this system, spectral methods are applied to perform a complete stability analysis. Particularly, the method of cluster treatment of characteristic roots is used to determine stability boundaries in the space of the resonator parameters. Based on this analysis, a methodology to select the resonator parameters is proposed in order to guarantee desirable suppression characteristics and to provide safe stability margins. An example case study is included to demonstrate these analytical results.
Predictor-based stabilization for chained form systems with input time delay
Directory of Open Access Journals (Sweden)
Mnif Faïçal
2016-12-01
Full Text Available This note addresses the stabilization problem of nonlinear chained-form systems with input time delay. We first employ the so-called σ-process transformation that renders the feedback system under a linear form. We introduce a particular transformation to convert the original system into a delay-free system. Finally, we apply a state feedback control, which guarantees a quasi-exponential stabilization to all the system states, which in turn converge exponentially to zero. Then we employ the so-called -type control to achieve a quasi-exponential stabilization of the subsequent system. A simulation example illustrated on the model of a wheeled mobile robot is provided to demonstrate the effectiveness of the proposed approach.
Robust Delay-dependent H∞ Consensus Control for Multi-agent Systems with Input Delays
Institute of Scientific and Technical Information of China (English)
LI Zhen-Xing; JI Hai-Bo
2014-01-01
This paper investigates the consensus control for multi-agent systems subject to external disturbances, input delays and model uncertainties of networks. By defining an appropriate controlled output, we transform this question into a robust H∞control problem. Then, we give two criteria to judge the consensusability of closed-loop multi-agent systems and present a cone-complementary linearization algorithm to get the state feedback controller′s parameters. Finally, numerical examples are given to show the effectiveness of the proposed consensus protocols.
Directory of Open Access Journals (Sweden)
Qiankun Song
2007-06-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Directory of Open Access Journals (Sweden)
Cao Jinde
2007-01-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Dynamical properties induced by state-dependent delays in photonic systems
Martínez-Llinàs, Jade; Porte, Xavier; Soriano, Miguel C.; Colet, Pere; Fischer, Ingo
2015-06-01
In many dynamical systems and complex networks time delays appear naturally in feedback loops or coupling connections of individual elements. Moreover, in a whole class of systems, these delay times can depend on the state of the system. Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies. Here we fill this gap by introducing a conceptually simple photonic system that exhibits dynamics of self-organised switching between two loops with two different delay times, depending on the state of the system. On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays. Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.
PID Controller Stabilization for First-order Integral Processes with Time Delay
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Due to the widespread application of the PID controller in industrial control systems, it is desirable to know the complete set of all the stabilizing PID controllers for a given plant before the controller design and tuning. In this paper,the stabilization problems of the classical proportionalintegral-derivative (PID) controller and the singleparameter PID controller (containing only one adjustable parameter) for integral processes with time delay are investigated, respectively. The complete set of stabilizing parameters of the classical PID controller is determined using a version of the Hermite-Biehler Theorem applicable to quasipolynomials. Since the stabilization problem of the single-parameter PID controller cannot be treated by the Hermite-Biehler Theorem, a simple method called duallocus diagram is employed to derive the stabilizing range of the single-parameter PID controller. These results provide insight into the tuning of the PID controllers.
Stabilization and PID tuning algorithms for second-order unstable processes with time-delays.
Seer, Qiu Han; Nandong, Jobrun
2017-03-01
Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.
Finite-time stabilization control for discontinuous time-delayed networks: New switching design.
Zhang, Ling-Ling; Huang, Li-Hong; Cai, Zuo-Wei
2016-03-01
This paper discusses the finite-time stabilization problem for time-varying delayed neural networks (DNNs) with discontinuous activation functions. By using fixed point theory and set-valued analysis, we establish the existence theorem of equilibrium point. In order to stabilize the states of this class of discontinuous DNNs in finite time, we design two different kinds of switching controllers which are described by discontinuous functions. Under the framework of Filippov solutions, several new and effective criteria are derived to realize finite-time stabilization of discontinuous DNNs based on the famous finite-time stability theory. Besides, the upper bounds of the settling time of stabilization are estimated. Numerical examples are finally provided to illustrate the correctness of the proposed design method and theoretical results.
Liu, Shuang; Zhao, Shuang-Shuang; Wang, Zhao-Long; Li, Hai-Bin
2015-01-01
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results. Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).
Yuan, Rong
2007-06-01
In this paper, we study almost periodic logistic delay differential equations. The existence and module of almost periodic solutions are investigated. In particular, we extend some results of Seifert in [G. Seifert, Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence, J. Differential Equations 164 (2000) 451-458].
Directory of Open Access Journals (Sweden)
Cheng Gong
2014-01-01
Full Text Available This paper investigates the H∞ filtering problem of discrete singular Markov jump systems (SMJSs with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on H∞-disturbance attenuation is presented, in which both stability and prescribed H∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependent H∞ filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI. Finally, an example is given to illustrate the effectiveness of the result.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one.It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under thes...
Institute of Scientific and Technical Information of China (English)
谢惠琴; 王全义
2004-01-01
In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1, 2,..., n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Directory of Open Access Journals (Sweden)
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Stability and attractive basins of multiple equilibria in delayed two-neuron networks
Institute of Scientific and Technical Information of China (English)
Huang Yu-Jiao; Zhang Hua-Guang; Wang Zhan-Shan
2012-01-01
Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r ≥ 1) corner points is studied.Sufficient conditions are established for checking the existence of (2r + 1)2 equilibria in delayed recurrent neural networks.Under these conditions,(r + 1)2 equilibria are locally exponentially stable,and (2r + 1)2 - (r + 1)2 - r2 equilibria are unstable.Attractive basins of stable equilibria are estimated,which are larger than invariant sets derived by decomposing state space.One example is provided to illustrate the effectiveness of our results.
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays
Directory of Open Access Journals (Sweden)
Emma Delgado
2016-04-01
Full Text Available We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency.
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.
Observer-based robust stabilization for uncertain systems with unknown time-varying delay
Institute of Scientific and Technical Information of China (English)
Peigang JIANG; Chunwen LI
2004-01-01
This paper focuses on the problem of robust stabiiization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI.The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.
Directory of Open Access Journals (Sweden)
Wenzhen Gan
2013-01-01
Full Text Available This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.
Stability of PID-Controlled Linear Time-Delay Feedback Systems
Martelli, Gianpasquale
2008-01-01
The stability of feedback systems consisting of linear time-delay plants and PID controllers has been investigated for many years by means of several methods, of which the Nyquist criterion, a generalization of the Hermite-Biehler Theorem, and the root location method are well known. The main purpose of these researches is to determine the range of controller parameters that allow stability. Explicit and complete expressions of the boundaries of these regions and computation procedures with a finite number of steps are now available only for first-order plants, provided with one time delay. In this note, the same results, based on Pontryagin's studies, are presented for arbitrary-order plants.
Manivannan, R; Samidurai, R; Cao, Jinde; Alsaedi, Ahmed; Alsaadi, Fuad E
2017-03-01
This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly (Q,S,R)-γ-dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network. Copyright © 2016 Elsevier Ltd. All rights reserved.
Stability of linear delay differential equations a numerical approach with Matlab
Breda, Dimitri; Vermiglio, Rossana
2015-01-01
This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is t...
Asymptotical stability of stochastic neural networks with multiple time-varying delays
Zhou, Xianghui; Zhou, Wuneng; Dai, Anding; Yang, Jun; Xie, Lili
2015-03-01
The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays.
Yi, Zhang; Tan, K K
2002-07-01
The Lotka-Volterra model of neural networks, derived from the membrane dynamics of competing neurons, have found successful applications in many "winner-take-all" types of problems. This paper studies the dynamic stability properties of general Lotka-Volterra recurrent neural networks with delays. Conditions for nondivergence of the neural networks are derived. These conditions are based on local inhibition of networks, thereby allowing these networks to possess a multistability property. Multistability is a necessary property of a network that will enable important neural computations such as those governing the decision making process. Under these nondivergence conditions, a compact set that globally attracts all the trajectories of a network can be computed explicitly. If the connection weight matrix of a network is symmetric in some sense, and the delays of the network are in L2 space, we can prove that the network will have the property of complete stability.
Robust Stability Analysis and Synthesis for Switched Discrete-Time Systems with Time Delay
Directory of Open Access Journals (Sweden)
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.
Stability and periodicity of solutions for delay dynamic systems on time scales
Directory of Open Access Journals (Sweden)
Zhi-Qiang Zhu
2014-04-01
Full Text Available This article concerns the stability and periodicity of solutions to the delay dynamic system $$ x^{\\triangle}(t=A(t x(t + F(t, x(t, x(g(t+C(t $$ on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, by using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solution is unique. In particular, the periodic solution is positive under proper assumptions.
Stability analysis of delayed cellular neural networks with and without noise perturbation
Institute of Scientific and Technical Information of China (English)
ZHANG Xue-juan; WANG Guan-xiang; LIU Hua
2008-01-01
The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied.After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system,we further investigate the case with noise perturbation.When DCNN is perturbed by external noise,the system is globally stable.An important fact is that,when the system is perturbed by internal noise,it is globally exponentially stable only if the total noise strength is within a certain bound.This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y＇(t) = λy(t) + μy(t - τ) with τ ＞ 0 and λ ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A-stable LM methods the upper bound for the norm of the n -th power of square matrix grows linearly with the order of the matrix.
Dynamical stability analysis of delayed recurrent neural networks with ring structure
Zhang, Huaguang; Huang, Yujiao; Cai, Tiaoyang; Wang, Zhanshan
2014-04-01
In this paper, multistability is discussed for delayed recurrent neural networks with ring structure and multi-step piecewise linear activation functions. Sufficient criteria are obtained to check the existence of multiple equilibria. A lemma is proposed to explore the number and the cross-direction of purely imaginary roots for the characteristic equation, which corresponds to the neural network model. Stability of all of equilibria is investigated. The work improves and extends the existing stability results in the literature. Finally, two examples are given to illustrate the effectiveness of the obtained results.
Ion, Anca Veronica
2010-01-01
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic solutions. Some stability results for the equilibria are also presented in these works, but they are incomplete and contain some errors. Our work aims to complete and to bring corrections to those results. Both Lyapunov first order approximation method and second Lyapunov method are used.
Wu, Yuanyuan; Cao, Jinde; Alofi, Abdulaziz; Al-Mazrooei, Abdullah; Elaiw, Ahmed
2015-09-01
This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results.
Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition
Directory of Open Access Journals (Sweden)
Nengwei Zhang
2014-01-01
Full Text Available Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
Multiple μ-stability of neural networks with unbounded time-varying delays.
Wang, Lili; Chen, Tianping
2014-05-01
In this paper, we are concerned with a class of recurrent neural networks with unbounded time-varying delays. Based on the geometrical configuration of activation functions, the phase space R(n) can be divided into several Φη-type subsets. Accordingly, a new set of regions Ωη are proposed, and rigorous mathematical analysis is provided to derive the existence of equilibrium point and its local μ-stability in each Ωη. It concludes that the n-dimensional neural networks can exhibit at least 3(n) equilibrium points and 2(n) of them are μ-stable. Furthermore, due to the compatible property, a set of new conditions are presented to address the dynamics in the remaining 3(n)-2(n) subset regions. As direct applications of these results, we can get some criteria on the multiple exponential stability, multiple power stability, multiple log-stability, multiple log-log-stability and so on. In addition, the approach and results can also be extended to the neural networks with K-level nonlinear activation functions and unbounded time-varying delays, in which there can store (2K+1)(n) equilibrium points, (K+1)(n) of them are locally μ-stable. Numerical examples are given to illustrate the effectiveness of our results.
Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure
Energy Technology Data Exchange (ETDEWEB)
Xu Rui [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang 050003, Hebei Province (China); Department of Applied Mathematics, School of Science, Xi' an Jiaotong University, Xi' an 710049 (China)], E-mail: rxu88@yahoo.com.cn; Ma Zhien [Department of Applied Mathematics, School of Science, Xi' an Jiaotong University, Xi' an 710049 (China)
2008-11-15
A ratio-dependent predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. By analyzing the characteristic equations, the local stability of a positive equilibrium and a boundary equilibrium is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium when {tau} = {tau}{sub 0}. By using an iteration technique, sufficient conditions are derived for the global attractivity of the positive equilibrium. By comparison arguments, sufficient conditions are obtained for the global stability of the boundary equilibrium. Numerical simulations are carried out to illustrate the main results.
Liu, Xiwei; Chen, Tianping
2016-03-01
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent real-valued system. The network model is described by a continuous-time equation. There are two main differences of this paper with previous works: 1) time delays can be asynchronous, i.e., delays between different nodes are different, which make our model more general and 2) we prove the exponential convergence directly, while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence. Using three generalized norms, we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex-valued neural networks. These conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons; so previous works of other researchers can be extended. Finally, some numerical simulations are given to demonstrate the correctness of our obtained results.
Derebaşı, Muhammet Burak
2015-01-01
Worldwide, there is an increasing interest to study social media dependency. Currently, most of the researches compare social media dependency with other dependencies such as substance abuse and gambling. Although, there is limited research to investigate the effect of personality on social media dependency. Therefore, the main aim of the current study was to examine the predictor roles of narcissism, perceived parenting styles and delay of gratification on social media dependency. A total of...
On global exponential stability of positive neural networks with time-varying delay.
Hien, Le Van
2017-03-01
This paper presents a new result on the existence, uniqueness and global exponential stability of a positive equilibrium of positive neural networks in the presence of bounded time-varying delay. Based on some novel comparison techniques, a testable condition is derived to ensure that all the state trajectories of the system converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.
Directory of Open Access Journals (Sweden)
Jing Wang
2012-01-01
Full Text Available The stabilization problem of a wireless networked control system is considered in this paper. Both time delay and packet loss exist simultaneously in the wireless network. The system is modeled as an asynchronous dynamic system (ADS with unstable subsystems. A sufficient condition for the system to be stable is presented. A numerical example is given to demonstrate the effectiveness of the proposed approach.
Wenzhen Gan; Canrong Tian; Qunying Zhang; Zhigui Lin
2013-01-01
This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show...
Robust Output Stabilization of Time-Varying Input Delay Systems using Attractive Ellipsoid Method
Polyakov, Andrey; Poznyak, Alexander; Richard, Jean-Pierre
2013-01-01
International audience; The problem of output control design for linear system with unknown and time-varying input delay, bounded exogenous disturbances and bounded deterministic measurement noises is considered. The prediction technique is combined with Luenberger-like observer design in order to provide the stabilizing output feedback. The scheme of parameters tuning for reduction of measurement noises effect and exogenous disturbances effects is developed basing on Attractive Ellipsoids Me...
Exponential stability of time-delay systems via new weighted integral inequalities
Hien, L. V.; Trinh, H.
2015-01-01
In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponential stability analysis for some classes of time-delay systems in the framework of linear matrix inequ...
Stability and Sensitive Analysis of a Model with Delay Quorum Sensing
Directory of Open Access Journals (Sweden)
Zhonghua Zhang
2015-01-01
Full Text Available This paper formulates a delay model characterizing the competition between bacteria and immune system. The center manifold reduction method and the normal form theory due to Faria and Magalhaes are used to compute the normal form of the model, and the stability of two nonhyperbolic equilibria is discussed. Sensitivity analysis suggests that the growth rate of bacteria is the most sensitive parameter of the threshold parameter R0 and should be targeted in the controlling strategies.
Impulsive stabilization and synchronization of a class of chaotic delay systems.
Li, Chuandong; Liao, Xiaofeng; Yang, Xiaofan; Huang, Tingwen
2005-12-01
The problems of control and synchronization of a class of chaotic systems with time delay via the impulsive control approach are investigated. Based on the Lyapunov-like stability theory for impulsive functional differential equations, several sufficient conditions are derived to guarantee chaos control and synchronization. Furthermore, we address the chaos quasisynchronization in the presence of single-parameter mismatch. Several illustrated examples are also given to show the effectiveness of the proposed methods.
Schlesner, J; Amann, A; Janson, N B; Just, W; Schöll, E
2003-12-01
We present a scheme to stabilize high-frequency domain oscillations in semiconductor superlattices by a time-delayed feedback loop. Applying concepts from chaos control theory we propose to control the spatiotemporal dynamics of fronts of accumulation and depletion layers which are generated at the emitter and may collide and annihilate during their transit, and thereby suppress chaos. The proposed method only requires the feedback of internal global electrical variables, viz., current and voltage, which makes the practical implementation very easy.
Institute of Scientific and Technical Information of China (English)
Ligang WU; Changhong WANG; Huijun GAO; Qingshuang ZENG
2006-01-01
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system;next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.
Wu, Qianqian; Tian, Tianhai
2016-08-24
To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. Among them, a widely used approach is delayed reaction for simplifying multistep reactions. However, recent research results suggest that a delayed reaction with constant time delay is unable to describe multistep reactions accurately. To address this issue, we propose a novel approach using state-dependent time delay to approximate multistep reactions. We first use stochastic simulations to calculate time delay arising from multistep reactions exactly. Then we design algorithms to calculate time delay based on system dynamics precisely. To demonstrate the power of proposed method, two processes of mRNA degradation are used to investigate the function of time delay in determining system dynamics. In addition, a multistep pathway of metabolic synthesis is used to explore the potential of the proposed method to simplify multistep reactions with nonlinear reaction rates. Simulation results suggest that the state-dependent time delay is a promising and accurate approach to reduce model complexity and decrease the number of unknown parameters in the models.
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.
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach.
ASYMPTOTIC STABILITY PROPERTIES OF θ-METHODS FOR THE MULTI-PANTOGRAPH DELAY DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
Dong-song Li; Ming-zhu Liu
2004-01-01
This paper deals with the asymptotic stability analysis of θ - methods for multi-pantograph delay differential equation u'(t)=λu(t)+lΣi=1μiu(qit),0＜ql＜ql-1＜…＜ql＜1,/u(0)=u0.Here λ,μ1,…,μl,u0∈C.In recent years stability properties of numerical methods for this kind of equation has been studied by numerous authors. Many papers are concerned with meshes with fixed stepsize. In general the developed techniques give rise to non-ordinary recurrence relation. In this work, instead, we study constrained variable stpesize schemes, suggested by theoretical and computational reasons, which lead to a non-stationary difference equation.A general theorem is presented which can be used to obtain the characterization of the stability regions of θ - methods.
Stability of equilibrium and periodic solutions of a delay equation modeling leukemia
Ion, Anca-Veronica
2010-01-01
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of periodic solutions emerged by Hopf bifurcation from a certain equilibrium point. We give the algorithm for approximating a center manifold at a typical point (in the parameter space) of Hopf bifurcation (and an unstable manifold in the vicinity of such a point, where such a manifold exists). Then we find the normal form of the equation restricted to the center manifold, by computing the first Lyapunov coefficient. The normal form allows us to establish the stability properties of the periodic solutions occurred by Hopf bifurcation.
Stability and synchronization analysis of inertial memristive neural networks with time delays.
Rakkiyappan, R; Premalatha, S; Chandrasekar, A; Cao, Jinde
2016-10-01
This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.
Ge, Hong-xia; Meng, Xiang-pei; Cheng, Rong-jun; Lo, Siu-Ming
2011-10-01
In this paper, an extended car-following model considering the delay of the driver's response in sensing headway is proposed to describe the traffic jam. It is shown that the stability region decreases when the driver's physical delay in sensing headway increases. The phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. By applying the reductive perturbation method, we get the time-dependent Ginzburg-Landau (TDGL) equation from the car-following model to describe the transition and critical phenomenon in traffic flow. We show the connection between the TDGL equation and the mKdV equation describing the traffic jam.
Differential Frequency-dependent Delay from the Pulsar Magnetosphere
Hassall, T E; Weltevrede, P; Hessels, J W T; Alexov, A; Coenen, T; Karastergiou, A; Kramer, M; Keane, E F; Kondratiev, V I; van Leeuwen, J; Noutsos, A; Pilia, M; Serylak, M; Sobey, C; Zagkouris, K; Fender, R; Bell, M E; Broderick, J; Eisloffel, J; Falcke, H; Griessmeier, J -M; Kuniyoshi, M; Miller-Jones, J C A; Wise, M W; Wucknitz, O; Zarka, P; Asgekar, A; Batejat, F; Bentum, M J; Bernardi, G; Best, P; Bonafede, A; Breitling, F; Bruggen, M; Butcher, H R; Ciardi, B; de Gasperin, F; de Reijer, J -P; Duscha, S; Fallows, R A; Ferrari, C; Frieswijk, W; Garrett, M A; Gunst, A W; Heald, G; Hoeft, M; Juette, E; Maat, P; McKean, J P; Norden, M J; Pandey-Pommier, M; Pizzo, R; Polatidis, A G; Reich, W; Rottgering, H; Sluman, J; Tang, Y; Tasse, C; Vermeulen, R; van Weeren, R J; Wijnholds, S J; Yatawatta, S
2013-01-01
Some radio pulsars show clear drifting subpulses, in which subpulses are seen to drift in pulse longitude in a systematic pattern. Here we examine how the drifting subpulses of PSR B0809+74 evolve with time and observing frequency. We show that the subpulse period (P3) is constant on timescales of days, months and years, and between 14-5100 MHz. Despite this, the shapes of the driftbands change radically with frequency. Previous studies have concluded that, while the subpulses appear to move through the pulse window approximately linearly at low frequencies ( 820 MHz) near to the peak of the average pulse profile. We use LOFAR, GMRT, GBT, WSRT and Effelsberg 100-m data to explore the frequency-dependence of this phase step. We show that the size of the subpulse phase step increases gradually, and is observable even at low frequencies. We attribute the subpulse phase step to the presence of two separate driftbands, whose relative arrival times vary with frequency - one driftband arriving 30 pulses earlier at 2...
Li, Huiping; Shi, Yang
2012-10-01
This article focuses on the state-feedback ℋ∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton-Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ℋ∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ℋ∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
Partial eigenvalue assignment and its stability in a time delayed system
Singh, Kumar V.; Dey, Rajeeb; Datta, Biswa N.
2014-01-01
Active vibration control strategy is an effective way to control dangerous vibrations in a structure, caused by resonance and to manipulate the dynamics of vibrational response. Implementation of this strategy requires real-time computations of two feedback control matrices such that a small amount of eigenvalues of the associated quadratic matrix pencil are replaced by suitably chosen ones while the remaining large number of eigenvalues and eigenvectors remain unchanged ensuring the no spill-over. This mathematical problem is referred to as the Quadratic Partial Eigenvalue Assignment problem. The greatest challenge there is to solve the problems using the knowledge of only a small number of eigenvalues and eigenvectors that are computable using state-of-the-art techniques. This paper generalizes the earlier work on partial assignment to constant time-delay systems. Furthermore, a posterior stability analysis is carried out to identify the ranges of the time-delay that maintains the closed-loop assignment while keeping the stability of the infinite number of eigenvalues for the time-delayed systems. The practical features of the proposed methods are that it is implemented in the second-order setting itself using only those small number of eigenvalues and the eigenvectors that are to be assigned and the no spill-over is established by means of mathematical results. The results of our numerical experiments support the validity of our proposed methods.
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.
Effects of Time Delay on Stability of an Unstable State in a Bistable System with Correlated Noises
Institute of Scientific and Technical Information of China (English)
LI Chun; MEI Dong-Cheng
2011-01-01
@@ Effects of time delay on stability of an unstable state in a time-delayed bistable system are investigated.The analytic expression of the transition rate W(xu,τ)from unstable state xu to stable state x+ is derived.The numerical calculation results of W(xu,τ)indicate that W(xu,τ)decreases with the increasing multiplicative noise intensity, the additive noise intensi by and the strength of correlations between the multiplicative and the additive noise increase, but W(xu,τ)increases with increasing delay time.Namely, the multiplicative noise, the additive noise and the correlations between the multiplicative and the additive noises enhance the stability of the unstable state in the time-delayed bistable system but the stability is weakened by time delay.%Effects of time delay on stability of an unstable state in a time-delayed bistable system are investigated. The analytic expression of the transition rate W(xu, T) from unstable state xu to stable state x+ is derived. The numerical calculation results of W(xu, T) indicate that W(xu, T) decreases with the increasing multiplicative noise intensity, the additive noise intensity and the strength of correlations between the multiplicative and the additive noise increase, but W(xu, T) increases with increasing delay time. Namely, the multiplicative noise, the additive noise and the correlations between the multiplicative and the additive noises enhance the stability of the unstable state in the time-delayed bistable system but the stability is weakened by time delay.
Analysis of stability of a Power System by using Delay Static State Feedback
Directory of Open Access Journals (Sweden)
Sindy Paola Amaya
2012-12-01
Full Text Available This article presents the analysis of stability of a power system modeled as Infinite Bus Connected Generator with delay static state feedback. The model of the power system is described by nonlinear differential- algebraic equations. For controller design, we linealize the nonlinear differential-algebraic model around an operation point to obtain a lineal differential-algebraic model. As of this model obtains the Kronecker -Weierstrass model which designs the controller. To obtain the K gain of the controller outline inequalities matrix lineal (LMI's . Then it makes a study of the maximum delay that it supports in the state feedback. At the end of the article present the results and the conclusions.
Stability of a general delayed virus dynamics model with humoral immunity and cellular infection
Elaiw, A. M.; Raezah, A. A.; Alofi, A. S.
2017-06-01
In this paper, we investigate the dynamical behavior of a general nonlinear model for virus dynamics with virus-target and infected-target incidences. The model incorporates humoral immune response and distributed time delays. The model is a four dimensional system of delay differential equations where the production and removal rates of the virus and cells are given by general nonlinear functions. We derive the basic reproduction parameter R˜0 G and the humoral immune response activation number R˜1 G and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations.
Institute of Scientific and Technical Information of China (English)
CHEN Jun; CUI Bao-Tong; GAO Ming
2008-01-01
The global asymptotic stability of delayed Cohen-Grossberg neural networks with impulses is investigated. Based on the new suitable Lyapunov functions and the Jacobsthal inequality, a set of novel sufficient criteria are derived for the global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays and impulses.An illustrative example with its numerical simulations is given to demonstrate the effectiveness of the obtained results.
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2012-01-01
Full Text Available A modified Holling-Tanner predator-prey system with multiple delays is investigated. By analyzing the associated characteristic equation, the local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are established. Direction and stability of the periodic solutions are obtained by using normal form and center manifold theory. Finally, numerical simulations are carried out to substantiate the analytical results.
Spin-dependent delay time in ferromagnet/insulator/ferromagnet heterostructures
Energy Technology Data Exchange (ETDEWEB)
Xie, ZhengWei; Zheng Shi, De; Lv, HouXiang [College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610066, Sichuan (China)
2014-07-07
We study theoretically spin-dependent group delay and dwell time in ferromagnet/insulator/ferromagnet (FM/I/FM) heterostructure. The results indicate that, when the electrons with different spin orientations tunnel through the FM/I/FM junction, the spin-up process and the spin-down process are separated on the time scales. As the self-interference delay has the spin-dependent features, the variations of spin-dependent dwell-time and spin-dependent group-delay time with the structure parameters appear different features, especially, in low incident energy range. These different features show up as that the group delay times for the spin-up electrons are always longer than those for spin-down electrons when the barrier height or incident energy increase. In contrast, the dwell times for the spin-up electrons are longer (shorter) than those for spin-down electrons when the barrier heights (the incident energy) are under a certain value. When the barrier heights (the incident energy) exceed a certain value, the dwell times for the spin-up electrons turn out to be shorter (longer) than those for spin-down electrons. In addition, the group delay time and the dwell time for spin-up and down electrons also relies on the comparative direction of magnetization in two FM layers and tends to saturation with the thickness of the barrier.
Directory of Open Access Journals (Sweden)
Changjian Wang
2017-01-01
Full Text Available In this paper, we consider the input-to-stability for a class of stochastic neutral-type memristive neural networks. Neutral terms and S-type distributed delays are taken into account in our system. Using the stochastic analysis theory and Itô formula, we obtain the conditions of mean-square exponential input-to-stability for system. A numerical example is given to illustrate the correctness of our conclusions.
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.
Global stability of a delayed mosquito-transmitted disease model with stage structure
Directory of Open Access Journals (Sweden)
B. G. Sampath Aruna Pradeep
2015-01-01
Full Text Available This article presents a new eco-epidemiological deterministic delay differential equation model considering a biological controlling approach on mosquitoes, for endemic dengue disease with variable host (human and variable vector (Aedes aegypti populations, and stage structure for mosquitoes. In this model, predator-prey interaction is considered by using larvae as prey and mosquito-fish as predator. We give a complete classification of equilibria of the model, and sufficient conditions for global stability/global attractivity of some equilibria are given by constructing suitable Lyapunov functionals and using Lyapunov-LaSalle invariance principle. Also, numerical simulations are presented to show the validity of our results.
Hopf Bifurcation and Stability Analysis for a Predator-prey Model with Time-delay
Institute of Scientific and Technical Information of China (English)
CHEN Hong-bing
2015-01-01
In this paper, a predator-prey model of three species is investigated, the necessary and sucient of the stable equilibrium point for this model is studied. Further, by introduc-ing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.
Directory of Open Access Journals (Sweden)
Fei Yu
2009-01-01
Full Text Available Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.
Stability and Bifurcation in a Delayed Reaction-Diffusion Equation with Dirichlet Boundary Condition
Guo, Shangjiang; Ma, Li
2016-04-01
In this paper, we study the dynamics of a diffusive equation with time delay subject to Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady-state solution is investigated by applying Lyapunov-Schmidt reduction. The existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. The direction of Hopf bifurcation and stability of the bifurcating periodic solution are also investigated by means of normal form theory and center manifold reduction. Moreover, we illustrate our general results by applications to the Nicholson's blowflies models with one- dimensional spatial domain.
Time-dependent stabilization in AdS/CFT
Auzzi, Roberto; Gudnason, Sven Bjarke; Rabinovici, Eliezer
2012-01-01
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high freque...
Directory of Open Access Journals (Sweden)
Yuan Ren
2016-01-01
Full Text Available This paper analyzes the effects of time delay on the stability of the rotation modes for the magnetically suspended flywheel (MSFW with strong gyroscopic effects. A multi-input multioutput system is converted into a single-input single-output control system with complex coefficient by variable reconstruction, and the stability equivalence of the systems before and after variable reconstruction is proven. For the rotation modes, the stability limits and corresponding vibration frequencies are found as a function of nondimensional magnetic stiffness and damping and nondimensional parameters of rotor speed and time delay. Additionally, the relationship between cross feedback control system stability and time delay is investigated. And an effective phase compensation method based on cross-channel is further presented. Simulation and experimental results are presented to demonstrate the correctness of the stability analysis method and the superiority of the phase compensation strategy.
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.
Joint time and frequency dissemination network over delay-stabilized fiber optic links
Chen, Wei; Cheng, Nan; Xu, Dan; Yang, Fei; Gui, Youzhen; Cai, Haiwen
2015-01-01
A precise fiber-based time and frequency dissemination scheme for multiple users with a tree-like branching topology is proposed. Through this scheme, ultra-stable signals can be easily accessed online anywhere along the fiber without affecting other sites. The scheme is tested through an experiment, in which a modulated frequency signal and a synchronized time signal are transferred to multiple remote sites over a delay-stabilized fiber optic links that are over 50 km long. Results show that the relative stabilities are 5E-14@1s and 2E-17@10000s. Meanwhile, compared with each site, time synchronization precision is less than 80 ps. These results can pave the way to practical applications in joint time and frequency dissemination network systems.
Zhang, Jiangyan; Shen, Tielong
To analyze and synthesize time-delay systems with discontinuity, the framework of differential inclusion in the sense of Filippov is extended to functional differential inclusion. Based on the extension, the concept of Filippov solution is introduced for the time-delay systems with discontinuity at first, and then it is shown that both the Lyapunov stability and the LaSalle invariance principle results can be extended to such kind of systems. Moreover, by using the proposed analysis tools, a stabilization feedback design approach is proposed for a class of nonlinear time-delay systems with discontinuity. Simulation results of numerical examples are given to demonstrate the proposed control approaches.
Directory of Open Access Journals (Sweden)
Rachael K Walsh
Full Text Available Aedes albopictus, a species known to transmit dengue and chikungunya viruses, is primarily a container-inhabiting mosquito. The potential for pathogen transmission by Ae. albopictus has increased our need to understand its ecology and population dynamics. Two parameters that we know little about are the impact of direct density-dependence and delayed density-dependence in the larval stage. The present study uses a manipulative experimental design, under field conditions, to understand the impact of delayed density dependence in a natural population of Ae. albopictus in Raleigh, North Carolina. Twenty liter buckets, divided in half prior to experimentation, placed in the field accumulated rainwater and detritus, providing oviposition and larval production sites for natural populations of Ae. albopictus. Two treatments, a larvae present and larvae absent treatment, were produced in each bucket. After five weeks all larvae were removed from both treatments and the buckets were covered with fine mesh cloth. Equal numbers of first instars were added to both treatments in every bucket. Pupae were collected daily and adults were frozen as they emerged. We found a significant impact of delayed density-dependence on larval survival, development time and adult body size in containers with high larval densities. Our results indicate that delayed density-dependence will have negative impacts on the mosquito population when larval densities are high enough to deplete accessible nutrients faster than the rate of natural food accumulation.
Directory of Open Access Journals (Sweden)
Natarajan Meghanathan
2008-02-01
Full Text Available We present a detailed ns-2 based simulation analysis on four of the prominent mobile ad hoc network routing protocols: Dynamic Source Routing (DSR protocol, Associativity-Based Routing (ABR protocol, Flow- Oriented Routing Protocol (FORP and the Routelifetime Assessment Based Routing (RABR protocol. The simulations were conducted with and without transmission power control. We define transmission power control for a hop comprising of a sender and receiver as the problem of choosing the transmission power at the sender depending on the distance to the intended receiver. Route stability is quantified using the number of route transitions (route discoveries incurred for a source-destination session. We also define the network lifetime as the time of first node failure due to exhaustion of node battery power. Our simulation results indicate a stability versus {energy consumption-delay-network lifetime} tradeoff among the four routing protocols: FORP routes are more stable than RABR routes, which are more stable than ABR routes, which are more stable than DSR routes. With respect to the end-to-end delay per packet, network lifetime, the energy consumed per node and the energy consumed per packet, DSR is better than ABR, which is better than RABR, which is better than FORP. We observe this tradeoff for simulations conducted with and without transmission power control. Nevertheless, the crucial observation is that by using transmission power control, the tradeoff could be reduced: the higher the stability of the routing protocol, the larger is the magnitude of reduction in the energy consumption and improvement in the network lifetime.
Delay-Dependent Response in Weakly Electric Fish under Closed-Loop Pulse Stimulation.
Forlim, Caroline Garcia; Pinto, Reynaldo Daniel; Varona, Pablo; Rodríguez, Francisco B
2015-01-01
In this paper, we apply a real time activity-dependent protocol to study how freely swimming weakly electric fish produce and process the timing of their own electric signals. Specifically, we address this study in the elephant fish, Gnathonemus petersii, an animal that uses weak discharges to locate obstacles or food while navigating, as well as for electro-communication with conspecifics. To investigate how the inter pulse intervals vary in response to external stimuli, we compare the response to a simple closed-loop stimulation protocol and the signals generated without electrical stimulation. The activity-dependent stimulation protocol explores different stimulus delivery delays relative to the fish's own electric discharges. We show that there is a critical time delay in this closed-loop interaction, as the largest changes in inter pulse intervals occur when the stimulation delay is below 100 ms. We also discuss the implications of these findings in the context of information processing in weakly electric fish.
An improved LMI-based approach for stability of piecewise affine time-delay systems with uncertainty
Duan, Shiming; Ni, Jun; Galip Ulsoy, A.
2012-09-01
The stability problem for uncertain piecewise affine (PWA) time-delay systems is investigated in this article. It is assumed that there exists a known constant time delay in the system and the uncertainly is norm-bounded. Sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the Lyapunov-Krasovskii functional with a triple integration term. This approach handles switching based on the delayed states (in addition to the states) for a PWA time-delay system, considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches. The effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples.
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.
Uniqueness and stability of traveling waves for cellular neural networks with multiple delays
Yu, Zhi-Xian; Mei, Ming
2016-01-01
In this paper, we investigate the properties of traveling waves to a class of lattice differential equations for cellular neural networks with multiple delays. Following the previous study [38] on the existence of the traveling waves, here we focus on the uniqueness and the stability of these traveling waves. First of all, by establishing the a priori asymptotic behavior of traveling waves and applying Ikehara's theorem, we prove the uniqueness (up to translation) of traveling waves ϕ (n - ct) with c ≤c* for the cellular neural networks with multiple delays, where c* < 0 is the critical wave speed. Then, by the weighted energy method together with the squeezing technique, we further show the global stability of all non-critical traveling waves for this model, that is, for all monotone waves with the speed c
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.
Directory of Open Access Journals (Sweden)
Jing Li
2013-04-01
Full Text Available We study the uniform stabilization of a semilinear wave equation with variable coefficients and a delay term in the boundary feedback. The Riemannian geometry method is applied to prove the exponential stability of the system by introducing an equivalent energy function.
Dependence of stability of metastable superconductors on copper fraction
Energy Technology Data Exchange (ETDEWEB)
Elrod, S. A.; Lue, J. W.; Miller, J. R.; Dresner, L.
1980-12-01
The stability of composite superconductors operating in the metastable regime depends upon such factors as matrix resistivity, cooled surface dimensions, fraction of critical current, and volume fraction of stabilizer. By assuming constant thermophysical properties, we developed analytic expressions for the energy and voltage of the minimum propagating zone (MPZ). With other factors held constant, these expressions have been used to predict composite superconductor stability as a function of copper fraction: lower copper fractions lead to higher MPZ energies. MPZ voltages have been measured for three NbTi/Cu composites having different copper fractions and different critical current densities for several magnetic fields and transport currents. Experimental MPZ voltages have been used to calculate an effective heat transfer coefficient, which is subsequently used to calculate the MPZ energy. The experimental MPZ energies support the theoretical expectation that lower copper fractions lead to higher stability in the metastable regime.
On the angular dependence of the photoemission time delay in helium
Ivanov, I A; Lindroth, E; Kheifets, A S
2016-01-01
We investigate an angular dependence of the photoemission time delay in helium as measured by the RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) technique. The measured time delay $ \\tau_a=\\tau_W+\\tau_{cc} $ contains two distinct components: the Wigner time delay $\\tau_W$ and the continuum-continuum CC) correction $\\tau_{cc}$. In the case of helium with only one $1s\\to Ep$ photoemission channel, the Wigner time delay $\\tau_W$ does not depend on the photoelectron detection angle relative to the polarization vector. However, the CC correction $\\tau_{cc}$ shows a noticeable angular dependence. We illustrate these findings by performing two sets of calculations. In the first set, we solve the time-dependent Schr\\"odinger equation for the helium atom ionized by an attosecond pulse train and probed by an IR pulse. In the second approach, we employ the lowest order perturbation theory which describes absorption of the XUV and IR photons. Both calculations produce close resul...
An age-dependent population equation with diffusion and delayed birth process
Directory of Open Access Journals (Sweden)
G. Fragnelli
2005-01-01
Full Text Available We propose a new age-dependent population equation which takes into account not only a delay in the birth process, but also other events that may take place during the time between conception and birth. Using semigroup theory, we discuss the well posedness and the asymptotic behavior of the solution.
PERIODICITY IN A DELAYED SEMI-RATIO-DEPENDENT PREDATOR-PREY SYSTEM
Institute of Scientific and Technical Information of China (English)
DingXiaoquan
2005-01-01
A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper. By using a continuation theorem based on Gaines and Mawhin's coincidence degree,the global existence of positive periodic solution is studied. A set of easily verifiable sufficient conditions are obtained.
Hopf bifurcation in a partial dependent predator-prey system with delay
Energy Technology Data Exchange (ETDEWEB)
Zhao Huitao [Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093 (China); Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001 (China)], E-mail: taohuiz@sohu.com; Lin Yiping [Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093 (China)], E-mail: linyiping689@sohu.com
2009-10-30
In this paper, a partial dependent predator-prey model with time delay is studied by using the theory of functional differential equation and Hassard's method, the condition on which positive equilibrium exists and Hopf bifurcation occurs are given. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.
Hernandez, Eduardo; Pierri, Michelle; Wu, Jianhong
2016-12-01
We study the existence and uniqueness of C 1 + α-strict solutions for a general class of abstract differential equations with state dependent delay. We also study the local well-posedness of this type of problems on subspaces of C 1 + α ([ - p , 0 ] ; X). Some examples involving partial differential equations are presented.
EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.
MULTIPLE POSITIVE PERIODIC SOLUTIONS TO SINGULAR DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenvalue of the relevant linear operator. The results in this paper are optimal and totally generalize many present results.
Directory of Open Access Journals (Sweden)
Tianxiang Yao
2014-01-01
Full Text Available This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.
Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping
2014-11-01
In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.
The Application of Time-Delay Dependent H∞ Control Model in Manufacturing Decision Optimization
Directory of Open Access Journals (Sweden)
Haifeng Guo
2015-01-01
Full Text Available This paper uses a time-delay dependent H∞ control model to analyze the effect of manufacturing decisions on the process of transmission from resources to capability. We establish a theoretical framework of manufacturing management process based on three terms: resource, manufacturing decision, and capability. Then we build a time-delay H∞ robust control model to analyze the robustness of manufacturing management. With the state feedback controller between manufacturing resources and decision, we find that there is an optimal decision to adjust the process of transmission from resources to capability under uncertain environment. Finally, we provide an example to prove the robustness of this model.
Constraints on frequency-dependent violations of Shapiro delay from GW150914
Directory of Open Access Journals (Sweden)
Emre O. Kahya
2016-05-01
Full Text Available On 14th September 2015, a transient gravitational wave (GW150914 was detected by the two LIGO detectors at Hanford and Livingston from the coalescence of a binary black hole system located at a distance of about 400 Mpc. We point out that GW150914 experienced a Shapiro delay due to the gravitational potential of the mass distribution along the line of sight of about 1800 days. Also, the near-simultaneous arrival of gravitons over a frequency range of about 200 Hz within a 0.2 s window allows us to constrain any violations of Shapiro delay and Einstein's equivalence principle between the gravitons at different frequencies. From the calculated Shapiro delay and the observed duration of the signal, frequency-dependent violations of the equivalence principle for gravitons are constrained to an accuracy of O(10−9.
Su, T T; Jaklevic, B
2001-01-09
In response to DNA damage, fission yeast, mammalian cells, and cells of the Drosophila gastrula inhibit Cdk1 to delay the entry into mitosis. In contrast, budding yeast delays metaphase-anaphase transition by stabilization of an anaphase inhibitor, Pds1p. A variation of the second response is seen in Drosophila cleavage embryos; when nuclei enter mitosis with damaged DNA, centrosomes lose gamma-tubulin, spindles lose astral microtubules, chromosomes fail to reach a metaphase configuration, and interphase resumes without an intervening anaphase. The resulting polyploid nuclei are eliminated. The cells of the Drosophila gastrula can also delay metaphase-anaphase transition in response to DNA damage. This delay accompanies the stabilization of Cyclin A, a known inhibitor of sister chromosome separation in Drosophila. Unlike in cleavage embryos, gamma-tubulin remains at the spindle poles, and anaphase always occurs after the delay. Cyclin A mutants fail to delay metaphase-anaphase transition after irradiation and show an increased frequency of chromosome breakage in the subsequent anaphase. DNA damage delays metaphase-anaphase transition in Drosophila by stabilizing Cyclin A. This delay may normally serve to preserve chromosomal integrity during segregation. To our knowledge this is the first report of a metazoan metaphase-anaphase transition being delayed in response to DNA damage. Though mitotic progression is modulated in response to DNA damage in both cleaving and gastruating embryos of Drosophila, different mechanisms operate. These differences are discussed in the context of differential cell cycle regulation in cleavage and gastrula stages.
Delay time dependence of thermal effect of combined pulse laser machining
Yuan, Boshi; Jin, Guangyong; Ma, Yao; Zhang, Wei
2016-10-01
The research focused on the effect of delay time in combined pulse laser machining on the material temperature field. Aiming at the parameter optimization of pulse laser machining aluminum alloy, the combined pulse laser model based on heat conduction equation was introduced. And the finite element analysis software, COMSOL Multiphysics, was also utilized in the research. Without considering the phase transition process of aluminum alloy, the results of the numerical simulation was shown in this paper. By the simulation study of aluminum alloy's irradiation with combined pulse, the effect of the change in delay time of combined pulse on the temperature field of the aluminum alloy and simultaneously the quantized results under the specific laser spot conditions were obtained. Based on the results, several conclusions could be reached, the delay time could affect the rule of temperature changing with time. The reasonable delay time controlling would help improving the efficiency. In addition, when the condition of the laser pulse energy density is constant, the optimal delay time depends on pulse sequence.
Directory of Open Access Journals (Sweden)
Xueliang Liu
2012-01-01
Full Text Available This paper is concerned with a containment problem of networked fractional-order system with multiple leaders under a fixed directed interaction graph. Based on the neighbor rule, a distributed protocol is proposed in delayed communication channels. By employing the algebraic graph theory, matrix theory, Nyquist stability theorem, and frequency domain method, it is analytically proved that the whole follower agents will flock to the convex hull which is formed by the leaders. Furthermore, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is obtained. As a special case, the interconnection topology under the undirected case is also discussed. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.
Complete stability of delayed recurrent neural networks with Gaussian activation functions.
Liu, Peng; Zeng, Zhigang; Wang, Jun
2017-01-01
This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3(k) equilibrium points with 0≤k≤n, among which 2(k) and 3(k)-2(k) equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.
NON NEUROLOGICAL OUTCOME COMPARISON OF EARLY AND DELAYED SURGICAL STABILIZATION IN C-SPINE FRACTURES
Directory of Open Access Journals (Sweden)
T. G. B. Mahadewa
2014-01-01
Full Text Available Background: Non neurological outcome postsurgical stabilization in C-spine injury has not been reported. Non neurological outcome i.e. the risk of lung infection (pneumonia, systemic inflammation response syndrome (SIRS, length of postoperative care (LOPOC which can compromise the recovery process and treatment period. This study aims to investigate non neurological outcome comparison after early surgical stabilization (ESS and delayed surgical stabilization (DSS in patients with C-spine fractures. Methods: The author retrospectively reviews 59 of 108 consecutive patients who met the inclusion criteria with C-spine fractures who underwent surgical stabilization at the Sanglah General Hospital, between 2007 and 2010. Consisting of 25 patients underwent ESS and 34 patients were treated by DSS. The last follow up period range was 3-36 months. Non neurological outcome were evaluated and compared; the risk of pneumonia, SIRS and LOPOC. Results: Significant statistically between ESS and DSS in; the risk of pneumonia (ESS: DSS= 1:9 by Chi-square-test (p=0.023; the risk of SIRS (ESS: DSS= 1:11 by Chi-square-test (p=0.008; and the LOPOC (ESS: DSS= 6.84:9.97 by independent t-test (p=0.000. Application of ESS for C-spine fractures could provide early mobilization, prompt treatment and facilitate early rehabilitation thus significantly reduces complications due to prolong immobilization and reduces LOPOC. Conclussion: It can be concluded that the ESS strategy is effective and efficient thus may propose an option of surgical timing in C-spine fractures.
Abnormal Synchronizing Path of Delay-coupled Chaotic Oscillators on the Edge of Stability
Zhuo, Zhao; Fu, Zhong-Qian
2015-01-01
In this paper, the transition of synchronizing path of delay-coupled chaotic oscillators in a scale-free network is highlighted. Mainly, through the critical transmission delay makes chaotic oscillators be coupled on the edge of stability, we find that the transition of synchronizing path is \\emph{abnormal}, which is characterized by the following evidences: (a) synchronization process starts with low-degree rather than high-degree ones; (b) the high-degree nodes don't undertake the role of hub; (c) the synchronized subnetworks show a poor small-world property as a result of hubs absence; (d) the clustering synchronization behavior emerges even community structure is absent in the scale-free network. This abnormal synchronizing path suggests that the diverse synchronization behaviors occur in the same topology, which implies that the relationship between dynamics and structure of network is much more complicated than the common sense that the structure is the foundation of dynamics. Moreover, it also reveals ...
Tadepalli, Siva Kumar; Krishna Rao Kandanvli, V.; Kar, Haranath
2015-11-01
A recently reported paper (Ji, X., Liu, T., Sun, Y., and Su, H. (2011), 'Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities', International Journal of Systems Science, 42, 397-406) for the global asymptotic stability analysis and controller synthesis for a class of discrete linear time delay systems employing state saturation nonlinearities is reviewed. It is claimed in Ji, Liu, Sun and Su (2011) that a previous approach by Kandanvli and Kar (Kandanvli, V.K.R and Kar, H. (2009), 'Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach', Signal Processing, 89, 161-173) is recovered from their approach as a special case. It is shown that this claim is not justified.
Perceived object stability depends on multisensory estimates of gravity.
Barnett-Cowan, Michael; Fleming, Roland W; Singh, Manish; Bülthoff, Heinrich H
2011-04-27
How does the brain estimate object stability? Objects fall over when the gravity-projected centre-of-mass lies outside the point or area of support. To estimate an object's stability visually, the brain must integrate information across the shape and compare its orientation to gravity. When observers lie on their sides, gravity is perceived as tilted toward body orientation, consistent with a representation of gravity derived from multisensory information. We exploited this to test whether vestibular and kinesthetic information affect this visual task or whether the brain estimates object stability solely from visual information. In three body orientations, participants viewed images of objects close to a table edge. We measured the critical angle at which each object appeared equally likely to fall over or right itself. Perceived gravity was measured using the subjective visual vertical. The results show that the perceived critical angle was significantly biased in the same direction as the subjective visual vertical (i.e., towards the multisensory estimate of gravity). Our results rule out a general explanation that the brain depends solely on visual heuristics and assumptions about object stability. Instead, they suggest that multisensory estimates of gravity govern the perceived stability of objects, resulting in objects appearing more stable than they are when the head is tilted in the same direction in which they fall.
KARAT-LAMBDA - frequency dependent ray-traced troposphere delays for space applications
Hobiger, Thomas; Baron, Philippe
2014-05-01
Space-geodetic microwave techniques work under the assumption that the only dispersive, i.e. frequency dependent delay contribution is caused by the ionosphere. In general, the refractivity, even for the troposphere, is a complex quantity which can be denoted as N = N0 + (N'(f) + i N''(f)) where N0 is a frequency independent term, and N'(f) and N''(f) represent the complex frequency dependence. Thereby, the imaginary part can be used to derive the loss of energy (absorption) and the real part can be assigned to the changes in the propagation velocity (refraction) and thus describes the delay of an electromagnetic wave which propagates through that medium. Although the frequency dependent delay contribution appears to be of small order, one has to consider that signals are propagating through few kilometers of troposphere at high elevations to hundredths of kilometers at low elevations. Therefore, the Kashima Ray-Tracing package (Hobiger et al., 2008) has been modified (and named KARAT-LAMBDA) to enable the consideration of a frequency dependent refractivity. By using this tool, it was studied if and to which extent future space geodetic instruments are affected from dispersive troposphere delays. Moreover, a semi-empirical correction model for the microwave link of the Atomic Clock Ensemble in Space (ACES) has been developed, based on ray-tracing calculations with KARAT-LAMBDA. The proposed model (Hobiger et al., 2013) has been tested with simulated ISS overflights at different potential ACES ground station sites and it could be demonstrated that this model is capable to remove biases and elevation dependent features caused by the dispersive troposphere delay difference between the up-link and down-link. References: T. Hobiger, R. Ichikawa, T. Kondo, and Y. Koyama (2008), Fast and accurate ray-tracing algorithms for real-time space geodetic applications using numerical weather models, Journal of Geophysical Research, vol. 113, iss. D203027, pp. 1-14. T. Hobiger, D
Effects of size-dependent elasticity on stability of nanotweezers
Institute of Scientific and Technical Information of China (English)
A FARROKHABADI; A KOOCHI; A KAZEMI; M ABADYAN
2014-01-01
It is well-recognized that the electromechanical response of a nanostructure is affected by its element size. In the present article, the size dependent stability behavior and nanotweezers fabricated from nanowires are investigated by modified couple stress elasticity (MCSE). The governing equation of the nanotweezers is obtained by taking into account the presence of Coulomb and intermolecular attractions. To solve the equation, four techniques, i.e., the modified variational iteration method (MVIM), the monotonic iteration method (MIM), the MAPLE numerical solver, and a lumped model, are used. The variations of the arm displacement of the tweezers versus direct current (DC) voltage are obtained. The instability parameters, i.e., pull-in voltage and deflection of the system, are computed. The results show that size-dependency will affect the stability of the nanotweezers significantly if the diameter of the nanowire is of the order of the length scale. The impact of intermolecular attraction on the size-dependent stability of the system is discussed.
A differential equation with state-dependent delay from cell population biology
Getto, Philipp; Waurick, Marcus
2016-04-01
We analyze a differential equation, describing the maturation of a stem cell population, with a state-dependent delay, which is implicitly defined via the solution of an ODE. We elaborate smoothness conditions for the model ingredients, in particular vital rates, that guarantee the existence of a local semiflow and allow to specify the linear variational equation. The proofs are based on theoretical results of Hartung et al. combined with implicit function arguments in infinite dimensions. Moreover we elaborate a criterion for global existence for differential equations with state-dependent delay. To prove the result we adapt a theorem by Hale and Lunel to the C1-topology and use a result on metric spaces from Diekmann et al.
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.
Energy Technology Data Exchange (ETDEWEB)
Izuta, G.; Wagatsuma, T.; Watanabe, K. [Yamagata Univ. (Japan)
1998-09-30
In time-delay systems, change of time-delay influences the stability significantly. This paper proposes a method to solve the 2-disk mixed sensitivity specifications for multivariable time-delay control systems by using a generalized stabilizing controller. The existence of the solution depends on the existence of a stable rational polynomial scalar function satisfying the mixed sensitivity specifications. By using observer gain matrix of the generalized stabilizing controller, a free parameter and conventional Riccati equation, a method to obtain a product of an inner function and a diagonal matrix with a diagonal element of filter to be arbitrarily established for the moiety of the core of the compensating sensitivity function. Then, the design method of a controller to eliminate the pole on the imaginary axis of sensitivity weighting with zero point sensitivity matrix is proposed on the state space by the extension of the idea of disturbance compensation of the Smith`s procedure. The existence of the solution is indicated if the filter satisfies a certain condition and a method to obtain this filter is given. The effectiveness of this method is shown through numerical examples. 28 refs., 6 figs.