非线性随机时滞系统族的鲁棒稳定性

研究了不确定性的一族非线性随机时滞系统的指数稳定性,建立了这种系统的均 方指数稳定和几乎必然指数稳定的时滞相关的充分准则;然后应用这些充分条件到一类不确 定性的随机时滞神经网络,得到了这种神经网络指数稳定的实用判据.最后一个数值例子说 明所给准则的有效性.     

随机混沌时滞神经网络的指数同步

研究受随机扰动且具有时变时滞神经网络的指数同步. 根据Lyapunov稳定性理论结合线性矩阵不等式技巧, 通过构造含时滞的状态反馈控制器, 使得受到随机扰动的驱动系统和响应系统达到指数同步, 给出了随机时滞神经网络指数同步的新判据, 最后通过仿真验证了所用方法的有效性.     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

对带控制器饱和的Markovian跳跃双线性系统稳定时滞估计

研究了带有饱和控制器的时滞Markovian跳跃双线性系统随机镇定问题. 文章先给出了采用无记忆控制的相应无时滞系统局部指数稳定的充分性条件, 然后给出了采用该无记忆控制的时滞系统保持随机稳定性的最大时滞上界估计. 数值算例验证了该方法的有效性.     

时滞随机关联系统的群稳定性

在假定激励是参数白噪声的前提下, 基于箱体理论, 研究了无限维时滞随机关联系统中各子系统的内部联系. 利用向量Lyapunov 函数法, 研究了无限维时滞随机关联系统的群稳定性, 分别得到了无限维时滞非线性复合随机系统、无限维时滞弱耦合随机系统, 以及无限维时滞车辆跟随随机系统指数群稳定性的充分条件. 最后给出一个算例, 用以说明定理在实际中便于应用.     

脉冲时滞Hopfield神经网络的全局指数稳定性

研究一类具有脉冲控制的时滞Hopfideld神经网络的全局指数稳定性,通过Lyapunov-Krasovskii稳定性理论和Halanay不等式等方法,构造合适的Lyapunov泛函,利用不等式技巧得到了确保时滞神经网络在脉冲控制下全局指数稳定的一个充分条件,保证了Hofidd神经网络在脉冲控制下的全局指数稳定,并估计了系统的指数收敛率.为了便于计算和验证结论的有效性,给出一个简化的充分条件.最后通过数值实例的实验仿真证实了结论的有效性、可行性.     

具有时滞脉冲的线性随机时滞系统的均方指数稳定

本文研究了具有时滞脉冲的线性随机时滞系统的稳定性问题,基于Lyapunov函数和Razumikhin技巧,针对具有镇定型脉冲和反镇定型脉冲的线性随机时滞系统分别建立了系统均方指数稳定的充分条件,最后给出两个数值例子论证结果的有效性.     

随机细胞神经网络平衡点均方指数稳定性分析

主要利用Lyapunov 泛函方法研究带脉冲的随机时滞神经网络平衡点的均方指数稳定性。主要借助于不等式,随机分析理论给出主要结果。最后给出一数值算例证明结果的有效性。     

分布时滞随机偏微分系统的均方指数稳定性

针对一类同时具有分布时滞和维纳过程的随机偏微分系统, 首先基于It?o微分公式, 通过计算弱无穷小算 子, 得到了随机微分导数; 其次利用Green公式和积分不等式及Schur补引理对矩阵不等式进行处理; 然后对微分两 边积分并同时取数学期望处理随机交叉项; 获得了分布时滞随机偏微分系统是均方指数稳定的充分条件. 在此基础 上, 进一步考虑了离散变时滞和分布变时滞在一定约束情形下的分布时滞随机偏微分系统的均方指数稳定性问题. 最后给出仿真实例, 仿真结果表明所获得的线性矩阵不等式条件保证了系统的稳定性, 验证了所得结论的有效性.     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

非线性随机时滞系统的稳定性与应用

首先考虑了不确定性的一族非线笥随机时滞系统,建立了这种系统的均方指数稳定与几乎必须指数稳定的充分准则,其准则是时滞无关的,然后应用这些充分条件到一类不确定的随机时滞神经网络,得到了这咱神经网络指数稳定的产用判据。本文的结果是最近文献中某些结果的推广,最后一个数值例子说明的所给准则的有效性。     

Stabilization of stochastic delayed neural networks with Markovian switching

In this paper, the mean square exponential stabilization problem is investigated for a class of stochastic delayed neural networks with Markovian switching. After proposing an exponential stability condition, our attention is focused on the design of a state feedback controller such that the stochastic delayed neural networks with Markovian switching is exponentially stable in mean square. Several stabilization criteria, delay‐independent and delay‐dependent ones, which are expressed in terms of a set of linear matrix inequalities (LMIs), are proposed to stabilize the stochastic delayed neural networks with Markovian switching exponentially. The usefulness and applicability of the developed results are illustrated by means of two numerical examples. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential stability of stochastic high-order BAM neural networks with time delays and impulsive effects

In this paper, we consider the problem on exponential stability analysis of the stochastic impulsive high-order BAM neural networks with time delays. Through employing Lyapunov function method and stochastic bidirected halanay inequality, we constitute exponential stability of the stochastic impulsive high-order BAM neural networks with its estimated exponential convergence rate and feasible interval of impulsive strength. An example illustrates the main results.     

Stability analysis of stochastic recurrent neural networks with unbounded time-varying delays

In this paper, the stability analysis issue of stochastic recurrent neural networks with unbounded time-varying delays is investigated. By the idea of Lyapunov function and the semi-martingale convergence theorem, both pth moment exponential stability and almost sure exponential stability are obtained. Moreover, the M-matrix technique is borrowed to make the results more applicable. Our criteria can be used not only in the case of bounded delay but also in the case of unbounded delay. Some earlier results are improved and generalized. An example is also given to demonstrate our results.     

Novel robust stability criteria of discrete-time stochastic recurrent neural networks with time delay

The problem of robust global exponential stability is investigated for a class of stochastic uncertain discrete-time recurrent neural networks with time delay. In this paper, the midpoint of the time delay's variation interval is introduced, and the variation interval is divided into two subintervals. Then, by constructing a new Lyapunov–Krasovskii functional and checking its variation in the two subintervals, respectively, some novel delay-dependent stability criteria for the addressed neural networks are derived. Numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature.     

Mean square exponential stability of stochastic genetic regulatory networks with time-varying delays

In this paper, we study the mean square exponential stability of stochastic genetic regulatory networks with time-varying delays. Two kinds of time-varying delays are considered: one is differentiable with bounded delay derivative the other is continuous without constraints on the delay derivative. In order to investigate the mean square exponential stability in stochastic genetic regulatory networks, some novel rate-dependent/independent mean square exponential stability criteria are derived by constructing Lyapunov-Krasovskii functional. The sufficient conditions are given in terms of linear matrix inequalities. Moreover, illustrative examples are used to substantiate the effectiveness and less conservativeness of our results.