一类非线性组合大系统的稳定性

本文研究一类比较广泛的非线性组合大系统的稳定性问题.基于矩阵代数Riccati 方程存在对称正定解的新判据(引理2),给出了检验这类非线性组合大系统稳定性的新准 则,所给出的稳定性准则只涉及子系统的稳定性以及子系统之间的互联项,因此,当应用该准 则检验这类非线性组合大系统的稳定性时,避免了构造子系统以及大系统的Lyapunov函数 的困难.     

时变滞后随机大系统的稳定性：向量Lyapunov函数法

本文研究变系数、变时滞线性随机大系统的均方渐近稳定性，通过将Ｈａｌａｎａｙ不等式推广到高维空间、采用向量Ｌｙａｐｕｎｏｖ函数、运用Ｍ－矩阵等工具，得到了随机大系统的稳定性判据，文中模型考虑了子系统之间的交互随机干扰，所得稳定性判断是滞后无关的。     

离散双线性系统的稳定控制分析

对于一般离散双线性系统 ,本文提出了系统在线性反馈下的稳定性判据和最小吸引域 ,并给出了一种简单的控制方案 ,保证闭环系统在原点的一致渐近稳定性 .仿真结果证明了该方法的有效性 .所得稳定性判据对于选择合适的控制方案具有重要的指导意义 .     

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.     

Asymptotic stability criteria for a two-neuron network with different time delays

In this paper, the asymptotic stability of a two-neuron system with different time delays has been investigated. Some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of Lyapunov functional. For local asymptotic stability, some elegant criteria are also obtained by the Nyquist criteria. We find that one of them depends on the length of delays while the other ones do not. In the latter case, the delays are sometimes called harmless delays. The results obtained have leading significance in the study of neural networks composed of a large number of neurons with different time delays.     

针对准单边Lipschitz不确定非线性时滞系统的稳定性分析

研究了一类不确定非线性时滞系统的鲁棒稳定性. 准单边Lipschitz条件被介绍, 并被用于估计非线性向量函数在稳定性分析中的影响. 线性矩阵不等式形式的时滞无关/时滞相关稳定性判据被得到. 此外, 即使系统系数是不稳定的, 这些稳定性判据也是可利用的, 因为未必正定的准单边Lipschitz常数矩阵包含了很多非线性部分的有用信息. 数值实例证实了本文所获结果的有效性.     

基于增广Lyapunov泛函的Lurie时滞系统的绝对稳定性

对Lurie时滞系统的绝对稳定性问题进行了研究. 利用增广的Lyapunov泛函结合自由权矩阵方法, 得到了系统基于线性矩阵不等式(LMI)的时滞相关绝对稳定条件. 数值实例表明本文方法所得结果要优于现有文献中的结果.     

Stability analysis for T-S fuzzy systems with time-varying delay via free-matrix-based integral inequality

This paper is concerned with the problem of delay-dependent stability criteria for Takagi-Sugeno systems with time-varying delay. The less conservative delay-dependent stability criteria in terms of linear matrix inequalities are obtained by constructing a novel augmented Lyapunov-Krasovskii functional. In order to further improve the stability conditions, the free- matrix-based integral inequality is employed. Finally, several numerical examples on time-delay stability analysis are given to demonstrate the effectiveness and the merits of the proposed methods.     

无穷时滞神经网络的全局稳定性

本文研究具有无穷时滞的神经网络的全局稳定性问题。通过拓广泛函数微分方程理论中的Ｒａｚｕｍｉｋｈｉｎ思想，获得了无十分简洁的稳定性准则。     

Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components

In this paper, the problem of stability criteria of neural networks with two additive time-varying delay components is investigated. Some new delay-dependent stability criteria are derived in terms of linear matrix inequalities by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because reciprocally convex approach and convex polyhedron approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.