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。     

带有时滞的随机大系统的稳定性

本文对带有时滞的随机大系统给出了滞后无关均方渐近稳定性的定义和判据,所讨论的随机大系统具有随机互联结构。     

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.     

测度型脉冲时滞大系统的指数稳定性

本文借助加权范数型向量李雅普诺夫函数和积分型时滞比较原理，首次研究了测度型脉冲时滞线性时变大系统的指数稳定性。     

随机时滞系统的滤波稳定性与渐近性

本文对于用二阶向量差分方程描述的随机时滞系统,用增广差分方程的方法给出了数字滤波的稳定性定理和滤波误差方差阵的渐近性定理。释例计算表明,其结果与理论分析是一致的。     

时滞大系统的Robust稳定性

在本文中考虑了由非线性扰动子系统组成的时滞大系统的鲁棒稳定性问题，利用Ｌｙａｐｕｎｏｖ稳定性准则，对角占优矩阵的方法和结合矩阵Ｒｉｃｃａｔｉ方程，获得了系统指数稳定的充分判据，本文的结果改进并推广了文（４，６）的结果。     

时滞随机大系统的分散次优镇定

本文基于Ｒｉｃａａｔｉ矩阵方程、采用Ｌｙａｐｕｎｏｖ泛函研究具有时滞的Ｉｔｏ型随机大系统的分散次优镇定，建立了分散次优镇定的判据，给出了确定分散次优控制器的一个算法，这个算法以求解Ｌｙａｐｕｎｏｖ矩阵方程与Ｒｉｃｃａｔｉ矩阵方程为基础。文中命同了数值算例以说明本文算法的用法。     

随机大系统的大范围渐近随机关联稳定性

本文通过分析随机大系统的孤立子系统和互联结构,并通过引入两个互联矩阵,提出了非Ito型随机大系统的大范围渐近随机关联稳定性的概念,并给出了充分条件。所考虑的随机大系统的随机噪声服从大数定律。本文给出了一个例子以说明所得结果的可用性。     

线性多时变时滞系统的指数稳定性

本文基于一个新型滞后动态系统指数稳定性定理和两个准备引理, 采用 Lyapunov 函数稳定性分析新方法, 建立了线性多时变时滞系统保守性少的稳定性条件. 与文献中已有的一些结果不同, 所建立的稳定性条件不依赖于时变时滞的变化率. 因此, 所建立的结果适用于具有非常快变时滞的系统. 文中给出了一个例子展示所得结果好于直接采用标准的 Razumikhin 型条件所得的结果.     

基于LMI的混合时滞随机神经网络指数稳定性

为研究具有混合时滞的随机反馈神经网络的平衡解的稳定性问题,基于Lyapunov稳定性理论及It随机微分公式计算了随机神经网络得到在均方意义下的全局指数稳定性.利用网络模型中混合时滞的形式特点构造了新型的Lyapunov-Krasovskii泛函,并借助矩阵不等式分析技巧建立了新型采用线性矩阵不等式形式的判别条件,较已有采用矩阵范数形式的判别条件放宽了要求.线性矩阵不等式可以利用Matlab中提供的线性矩阵不等式进行计算验证,使得所得判别条件更加实用.最后给出了数值证明判别条件的有效性.     

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.     

Robustness of stability of nonlinear systems with stochastic delay perturbations

Suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential-functional equation. In this paper a sufficient condition is given so that the perturbed system remains exponentially stable. In the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable.     

Robust exponential stability conditions for retarded systems with Lipschitz nonlinear stochastic perturbations

This paper investigates robust mean‐square exponential stability of a class of uncertain stochastic state‐delayed systems with Lipschitz nonlinear stochastic perturbation. Based on Lyapunov–Krasovskii functional (LKF) method and free‐weighting matrix technique, some new delay‐dependent stability conditions are established in terms of linear matrix inequalities (LMIs). In order to reduce the conservatism, (1) the delay is divided into several segments, i.e. the delay decomposition method is applied; (2) cross terms estimation is avoided; (3) some information of the cross terms relationships which has not been involved in Reference (IET Control Theory Appl. 2008; 2(11):966–973) is considered. Moreover, from the mathematical point of view, the results obtained by free‐weighting matrix technique can be equivalently re‐formulated by simpler ones without involving any additional free matrix variables. The effectiveness of the method is demonstrated by numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.     

不确定切换时滞非线性系统状态切换的指数稳定性

利用状态依赖控制策略对切换信号进行设计,使得一类参数不确定时滞非线性切换系统指数稳定且具有一定的??∞抗干扰性能。利用Lyapunov-Krasovskii (LK)函数方法,以线性矩阵不等式组的方式,给出了稳定切换律存在的充分条件,并且该系统是指数稳定的。通过引入自由矩阵并结合积分不等式技巧,得到了保守性较低的稳定性条件。仿真算例表明了所提出方法的有效性和较低的保守性。     

一类随机人口发展系统的指数稳定性

对人口系统的讨论 ,通常的数学模型没有考虑外界环境对系统的影响 .在假设随机的外界环境对迁移产生扰动的条件下 ,给出Hilbert空间中一类随机时变人口发展系统 .对随机时变人口发展系统的均方稳定性和指数稳定性进行了讨论 .利用Burkholder_Davis_Gundy不等式 ,Gronwall引理和Kolmogorov不等式得到了均方稳定和指数稳定的充分条件 .最后提出如果生育率选作控制变量 ,系统仍然是均方和指数稳定的 ,并可进一步讨论它的最优控制问题     

Exponential stability of slowly varying discrete systems with multiple state delays

We give sufficient conditions for the exponential stability of a class of perturbed time‐varying difference equations with multiple delays and slowly varying coefficients. Under appropriate growth conditions on the perturbations, combined with the ‘freezing’ technique, we establish explicit conditions for global exponential stability. Copyright © 2012 John Wiley & Sons, Ltd.     

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.