Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays

This paper investigates robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. The delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional (LKF), some inequality techniques and stochastic stability theory, new delay-dependent stability criteria have been obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results.     

Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays

The synchronization problem for a class of complex dynamical networks with stochastic disturbances and probabilistic interval time-varying delays is investigated. Based on the stochastic analysis techniques and properties of the Kronecker product, some delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities (LMIs). The solvability of derived conditions depends not only on the size of the delay, but also on the probability of Bernoulli stochastic variables. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the global asymptotical stability analysis problem is considered for a class of Markovian jumping stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. An alternative delay-dependent stability analysis result is established based on the linear matrix inequality (LMI) technique, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Neither system transformation nor free weight matrix via Newton–Leibniz formula is required. Two numerical examples are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature.     

LMI approach to exponential stability of linear systems with interval time-varying delays

This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov–Krasovskii functional combined with the Newton–Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results.     

New robust stability criteria for uncertain neural networks with interval time-varying delays

In this paper, problem of robust stability of uncertain neural networks with interval time-varying delays has been investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional approach, a new delay-dependent stability criteria is presented in terms of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed method.     

无界可变延迟神经网络的一般稳定性(英文)

本文研究了无界延迟随机神经网络的稳定性,采用的主要技巧是Razumikhin方法,得到了p阶矩一般衰减率稳定性与几乎必然轨道一般衰减率稳定性.借助于M矩阵技巧使Razumikhin定理更便于应用.     

网络化马尔可夫跳变系统的鲁棒无源控制

针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性.     

具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性

研究了一类具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性.利用时变区间矩阵的分解技术、矩阵的Kronecker积的性质和Lyapunov函数法,得到了该系统均方鲁棒稳定的几个充分性条件.通过一个数值例子说明了所得的这些充分性条件的有效性和实用性.     

Exponential synchronization of complex dynamical networks with markovian jump parameters and stochastic delays and its application to multi-agent systems

This paper studies the synchronization problem of complex dynamical networks with stochastic delay which switches stochastically among several forms of time-varying delays. Both the discrete and distributed delays are considered, as well as the Markovian jump parameters. The occurrence probability distribution of the stochastic delay is assumed to be known in prior. By utilizing the Lyapunov–Krasovskii stability theory and stochastic analysis techniques, some sufficient exponential synchronization criteria are obtained, which depend not only on the size of delays, but also on the occurrence probability distribution of the stochastic delay. Moreover, the main results are successfully extended to multi-agent systems with stochastic delay. Several numerical examples are given to illustrate the feasibility and effectiveness of the proposed methods.     

Stochastic Stability Analysis for Switched Genetic Regulatory Networks with Interval Time-Varying Delays Based on Average Dwell Time Approach

In this article, the problem of stochastic stability analysis for switched stochastic genetic regulatory networks with interval time-varying delays based on average dwell time approach is investigated. By constructing the piecewise Lyapunov-Krasovskii functional, delay-dependent stability conditions are derived by using free-weighting matrix and convex combination approach. The derived stability conditions are expressed in terms of linear matrix inequalities which can be easily solved by using the MATLAB LMI control toolbox. Finally, numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed theoretical results.     

随机变时滞不确定性系统的鲁棒稳定性

本文讨论了一类随机变时滞不确定性线性微分系统的鲁棒稳定性。参数的不确定性表现为参数是随时间变化的未知函数,但是时范数有界的。利用线性矩阵不等式和Lyapunov函数的方法给出一些相关的稳定性结论。     

Stability analysis for stochastic jump systems with time-varying delay

This paper deals with the mean-square asymptotic stability of stochastic Markovian jump systems with time-varying delay. Based on a new stochastic inequality and convex analysis property, some novel stability conditions are presented. In the derivation, the information of the time-varying delay is retained and the estimation of it by the worst-case enlargement is not involved. Some special cases of the systems under consideration are also investigated. Illustrative examples are given to show the effectiveness of the proposed approach.     

Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks

This paper is concerned with the stability of n-dimensional stochastic differential delay systems with nonlinear impulsive effects. First, the equivalent relation between the solution of the n-dimensional stochastic differential delay system with nonlinear impulsive effects and that of a corresponding n-dimensional stochastic differential delay system without impulsive effects is established. Then, some stability criteria for the n-dimensional stochastic differential delay systems with nonlinear impulsive effects are obtained. Finally, the stability criteria are applied to uncertain impulsive stochastic neural networks with time-varying delay. The results show that, this convenient and efficient method will provide a new approach to study the stability of impulsive stochastic neural networks. Some examples are also discussed to illustrate the effectiveness of our theoretical results.     

Razumikhin method and exponential stability of hybrid stochastic delay interval systems

This paper deals with the exponential stability of hybrid stochastic delay interval systems (also known as stochastic delay interval systems with Markovian switching). The known results in this area (see, e.g., [X., Mao, Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Trans. Automat. Control 47 (10) (2002) 1604-1612]) require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics. The main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only. The Razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay.     

具有非线性扰动的不确定随机时变时滞系统的鲁棒镇定

本文研究了具有非线性扰动的不确定随机时变时滞系统的鲁棒镇定的问题.构造了适当的Lyapunov-Krasovskii泛函并利用自由权矩阵方法,借助于线性矩阵不等式(LMI)技术,设计了一个无记忆状态反馈控制器,并获得了不确定随机时变时滞系统的时滞依赖鲁棒镇定判据.数值例子及其仿真曲线表明所提出的理论结果是有效的.     

Stability and stabilization of switched linear discrete-time systems with interval time-varying delay

This paper deals with stability and stabilization of a class of switched discrete-time delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability and stabilization for the system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.     

Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays

The problem of stochastic robust stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are time-varying and norm-bounded. The time-delay factors are unknown and time-varying with known bounds. Based on Lyapunov–Krasovskii functional and stochastic analysis approaches, some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.     

Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

Abstract

A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Delay-dependent sufficient conditions for stability based on linear matrix inequalities (LMI's) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-dependent. The robustness results of such stability concept against all admissible uncertainties are also investigated. This new delay-dependent stability criteria is less conservative than the existing delay-independent stability conditions. An example is given to demonstrate the obtained results.     

Decentralized stability for switched nonlinear large-scale systems with interval time-varying delays in interconnections

In this paper, the problem of decentralized stability of switched nonlinear large-scale systems with time-varying delays in interconnections is studied. The time delays are assumed to be any continuous functions belonging to a given interval. By constructing a set of new Lyapunov–Krasovskii functionals, which are mainly based on the information of the lower and upper delay bounds, a new delay-dependent sufficient condition for designing switching law of exponential stability is established in terms of linear matrix inequalities (LMIs). The developed method using new inequalities for lower bounding cross terms eliminate the need for overbounding and provide larger values of the admissible delay bound. Numerical examples are given to illustrate the effectiveness of the new theory.