具混合时滞中立型随机神经网络均方渐近稳定性

研究了一类具有混合时滞和非线性干扰中立型不确定随机神经网络鲁棒稳定性,所考虑的不确定为范数有界,混合时滞由离散和分布时滞组成,借助李雅普诺夫函数和随机稳定性理论,利用伊藤公式,给出并证明了使系统鲁棒稳定的充分条件,所有结果以线性矩阵不等式的形式给出,数值算例表明了所给方法的有效性.     

时滞不确定性Markov切换线性随机微分系统的指数鲁棒稳定性

研究了一类时滞不确定性Markov切换随机微分系统的均方指数鲁棒随机稳定性\bd 系统中的时滞是时变的, 不确定项结构为范数有界, Markov切换是连续时间、离散状态的时齐Markov过程{\bf\!.} 利用随机Lyapunov函数方法和LMI技术, 得到了几个判定系统均方指数鲁棒随机稳定性的充分性条件\bd 一个数值例子说明了判据的有效性和可行性.     

含非线性扰动的变时滞中立系统时滞相关稳定性新条件

研究一类含非线性扰动和混合时变时滞的中立型系统时滞相关鲁棒稳定性问题.通过构造包含三重积分项的Lyapunov-Krasovskii的泛函,结合积分不等式和自由权矩阵技术,建立了基于线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关的稳定性新判据.判据扩大了系统稳定所允许的最大时滞上界范围,具有更低的保守性.利用MATLAB的LMI工具箱进行了数值仿真,仿真算例验证了所提出的稳定性判据的有效性.     

随机扰动神经网络的脉冲控制

脉冲控制具有响应速度快,鲁棒性和抗干扰能力好的特点,被广泛应用于参数随机扰动的动力学系统的控制.本文研究一类参数随机扰动的变时滞细胞神经网络在脉冲控制下的全局指数稳定性问题.利用Ly印unov稳定性理论和离散Halanay不等式技术手段,分别给出在脉冲控制下,参数随机扰动和无参数扰动的变时滞细胞神经网络全局指数稳定的充分条件.最后,通过数值算例说明所得结果.     

比较原理与一类具有时滞和马尔科夫切换的随机抛物方程组的稳定性分析（英文）北大核心CSCD

研究一类具有时滞和马尔科夫切换的随机抛物方程组的均方稳定性.通过建立比较原理,运用时滞微分不等式和随机分析技巧,获得了该系统的均方稳定、均方一致稳定、均方渐近稳定和均方指数稳定.最后,给出了主要定理的一个应用实例.     

比较原理与一类具有时滞和马尔科夫切换的随机抛物方程组的稳定性分析（英文）

研究一类具有时滞和马尔科夫切换的随机抛物方程组的均方稳定性.通过建立比较原理,运用时滞微分不等式和随机分析技巧,获得了该系统的均方稳定、均方一致稳定、均方渐近稳定和均方指数稳定.最后,给出了主要定理的一个应用实例.     

离散非线性时滞系统的鲁棒耗散控制

针对一类基于T-S模型表示的具有范数有界不确定性离散非线性时滞系统,研究了鲁棒耗散模糊控制问题.对可用T-S模糊模型表示的非线性时滞系统,考虑系统具有范数有界参数不确定性时,应用并行分布式控制方法,得到使得系统稳定且严格耗散的模糊耗散控制器存在的充分性条件.进而通过建立和求解LMI(线性矩阵不等式)约束的凸优化问题,给出了耗散控制律的设计方法.数值算例表明了此方法的可行性和有效性.     

随机切换拓扑下具有区间时变时滞的二阶离散多智能体系统的均方包含控制

研究随机切换拓扑下具有区间时变时滞的二阶离散多智能体系统的均方包含控制问题.通过一个变量变换,把原系统的均方包含控制问题转化为新系统的均方稳定性问题.根据随机稳定性理论和线性矩阵不等式的方法,给出了多智能体系统解决均方包含控制的充分条件.最后,仿真实例验证了理论结果的有效性.     

一类不确定时变时滞系统的鲁棒自适应稳定控制

研究了一类不确定时变时滞系统的鲁棒自适应稳定控制问题.系统包含多变时滞非线性扰动.基于Lyapunov稳定性理论和Lyapunov-K rasovsk ii型泛函设计出了一种无记忆的自适应状态反馈控制器,并证明了满足一定条件时,此控制器使得闭环系统最终一致有界.     

具有时滞的奇异扰动随机微分方程的均方指数稳定性

本文利用常数变易公式,随机过程数学期望的性质,矩阵范数,测度的相关理论以及不等式技巧,对一类具有时滞的奇异扰动随机微分方程的均方指数稳定性进行了讨论,得到了该类方程均方指数稳定的充分条件的代数判据.     

Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays

This paper deals with the exponential synchronization problem for a class of stochastic jumping chaotic neural networks with mixed delays and sector bounded nonlinearities. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time delays. By applying the Finsler’s Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent feedback controllers with sector nonlinearities are developed to achieve the synchronization in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve no free weighting matrices, the computational burden is largely reduced. One numerical example is provided to demonstrate the effectiveness of the theoretical results.     

Robust μ-stability analysis of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays

This paper investigates the global robust stability problem of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays and norm bounded parameter uncertainties. The structure variations at discrete time instances during the process of gene regulations known as hybrid genetic regulatory networks based on Markov process is proposed. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The concept of global robust μ-stability in the mean square for genetic regulatory networks is given. Based on Lyapunov function, stochastic theory and Itô’s differential formula, the stability criteria are presented in the form of linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the effectiveness of the main result.     

Exponential stability analysis of uncertain stochastic neural networks with multiple delays

This paper addresses the stability analysis problem for stochastic neural networks with parameter uncertainties and multiple time delays. The delays are time varying, and the parameter uncertainties are assumed to be norm bounded. A sufficient condition is derived such that for all admissible uncertainties, the considered neural network is globally exponentially stable in the mean square. The stability criterion is formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily checked in practice. Finally, a numerical example is provided to illustrate the proposed result.     

An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays

This paper deals with the problem of global exponential stability for a general class of stochastic high-order neural networks with mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both mixed time delays and Markovian switching. By employing a new Lyapunov–Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, and hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.     

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.     

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.     

网络化非周期采样控制系统的主动时间滞后控制: 随机脉冲切换系统方法

研究了一类带有随机丢包的非周期采样网络化控制系统的镇定问题.不同于传统观点往往将时滞看作系统稳定性的消极因素,考虑时间滞后对系统稳定性的积极影响, 并提出一个新颖的主动时间滞后控制方法来镇定该系统.为了分析时间滞后控制的积极作用并获得较低保守性的结论,首先把带随机丢包的非周期采样系统建模为带固定切换率的随机脉冲切换系统, 并在均方意义下提出一个新的分离引理用于分析随机脉冲切换系统的稳定性.然后,基于环 泛函方法和所提的分离引理,以线性矩阵不等式形式给出随机脉冲切换系统的均方稳定性判据.进一步,利用区间分割技术得到改进的均方稳定性判据.最后,利用一个经典的数值例子来验证所得稳定判据的有效性和所提方法的优势.     

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.     

Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

In this paper, the global exponential stability is investigated for a class of stochastic interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square. The criteria can be checked easily by the LMI control toolbox in Matlab. A numerical example is given to illustrate the effectiveness and improvement over some existing results.