区间矩阵稳定的新充分必要条件

本文讨论了对称区间矩阵的稳定性并给出了一个简单的充分必要条件，同时还讨论了线性时变区间矩阵和非线性时变区间矩阵的稳定性。     

关于区间矩阵的稳定性

文献[1]试图给出由端点矩阵的稳定性来保证区间矩阵的稳定性,文[2,3]指出文[1]的主要结果是错的.本文给出了端点矩阵的稳定性在一定条件下可以保证区间矩阵的稳定性,其结果比文[4]更精确,适用范围更大,且对具有分解的区间矩阵给出了其稳定及不稳定的充分条件.     

关于区间矩阵稳定性、可控性、可观性的充要条件的注记

该文是对区间矩阵稳定性、可观性及可控性的充要条件的若干注记,给出其饼算子 U的明确定义以及一个大区间矩阵分解成若干个子矩阵之饼的具体表达式.并进一步说明一 个区间矩阵(无穷多个矩阵)的稳定性、可控性、可观性等价于该区间矩阵中的有限个矩阵的 相应性质.建议了寻找这有限个矩阵的计算方法和步骤.     

区间离散Lurie系统的绝对稳定性

用Lyapunov函数研究了具有单调扇形限制的多非线性项的区间离散Lurie系统的鲁棒绝对稳定性, 给出了此类区间离散Lurie系统的鲁棒绝对稳定性的矩阵不等式形式的代数判据, 并与区间对称矩阵稳定性建立了联系.     

带有时滞的区间动力系统的鲁棒稳定性研究

给出了区间动力系统稳定性的相关概念,讨论了带有时滞的区间动力系统的鲁棒稳定性.通过构造控制矩阵和迭代相结合的方法,给出了一类带有时滞的区间动力系统鲁棒稳定的判别方法,并且给出了系统鲁棒稳定时参数取值的最大区间.将含有时滞的区间动力系统的稳定性转化为判别一个矩阵的稳定性,推广和改进了已有的结论.     

一类不确定系统的鲁棒稳定性分析

研究了一类不确定系统的稳定性问题, 以线性矩阵不等式(LMI)的形式给出了该类系统的鲁棒稳定条件, 并将该结果推广到区间系统的稳定性分析, 提出了研究区间系统稳定性问题的新方法, 给出了线性矩阵不等式形式的稳定判据, 该判据将区间系统的稳定性问题转化为一类线性矩阵不等式的可解问题. 最后通过仿真算例验证了本文结果具有更小的保守性.     

区间矩阵稳定的充分条件

讨论几类区间矩阵的稳定性，仅用区间矩阵元素的简单关系，获得了几个新的简单实用的充分条件。     

离散区间系统的鲁棒稳定性分析

本文主要研究了离散区间系统的稳定性问题,以线性矩阵不等式的形式给出了离散区间系统鲁棒稳定性的充分条件,最后通过仿真验证了该方法是行之有效的。     

关于时变区间矩阵的稳定性研究

本文对无界时变区间矩阵Ｎ［ Ｐ（ｔ），Ｑ（ｔ）］的稳定性进行了研究，给出了无界时 对变区间矩阵和具有分解的时变区间矩阵Ｎ［Ｐ（ｔ），Ｑ（ｔ）］稳定的充分条件，推广和改进了文［１，２］的工作。     

广义区间动力系统的稳定性分析

考虑广义区间动力系统的稳定性问题 .利用矩阵测度的有关性质 ,得到了广义区间动力系统稳定的充分条件 ,该充分条件保证所考虑的广义区间动力系统正则 ,无脉冲且稳定 .     

线性时变系统的区间稳定性和鲁棒稳定性

用矩阵测度研究了线性时变系统的区间稳 定性和具有非线性时变摄动的线性时变系统的鲁棒稳定性,得到了它们稳定的判别准则,所 得结果与文\[1~5\]的结果互不包含．     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.     

Stability of interval matrix polynomial in continuous and discrete cases

Sufficient conditions of asymptotic stability of interval matrix polynomial of both continuous and discrete cases are given. These conditions are presented in terms of the positive definiteness of either an (ln × ln) or (l × l) Hermitian and interval matrix. Therefore, the computation of the determinant interval polynomial is avoided.     

A survey of linear matrix inequality techniques in stability analysis of delay systems

Recent years have witnessed a resurgence of research interests in analysing the stability of time-delay systems. Many results have been reported using a variety of approaches and techniques. However, much of the focus has been laid on the use of the Lyapunov–Krasovskii theory to derive sufficient stability conditions in the form of linear matrix inequalities. The purpose of this article is to survey the recent results developed to analyse the asymptotic stability of time-delay systems. Both delay-independent and delay-dependent results are reported in the article. Special emphases are given to the issues of conservatism of the results and computational complexity. Connections of certain delay-dependent stability results are also discussed.     

New results on stability of singular stochastic Markov jump systems with state‐dependent noise

This paper aims to develop the stability theory for singular stochastic Markov jump systems with state‐dependent noise, including both continuous‐time and discrete‐time cases. The sufficient conditions for the existence and uniqueness of a solution to the system equation are provided. Some new and fundamental concepts such as non‐impulsiveness and mean square admissibility are introduced, which are different from those of other existing works. By making use of the ‐representation technique and the pseudo inverse E⁺ of a singular matrix E, sufficient conditions ensuring the system to be mean square admissible are established in terms of strict linear matrix inequalities, which can be regarded as extensions of the corresponding results of deterministic singular systems and normal stochastic systems. Practical examples are given to demonstrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

不确定广义线性时变系统的鲁棒稳定和二次稳定

针对不确定广义线性时变系统,采用矩阵不等式的分析方法,提出不确定广义线性时变系统鲁棒稳定和二次稳定的概念.建立该类系统的矩阵不等式,将该类系统的鲁棒控制问题转化为求解矩阵不等式问题,得到该类系统鲁棒稳定和二次稳定的充分必要条件,并给出一种状态反馈鲁棒镇定控制器的设计方法.最后,通过数值算例表明了所提出方法的可行性.     

Hopfield神经网络系统的全局稳定性分析

研究一类Hopfield神经网络系统的平衡状态的存在性、唯一性与全局稳定性, 这类系统放弃了以前对激励函数的有界性、单调性和可微性要求. 利用M矩阵理论, 通过构造适当的Lyapunov函数, 得到了系统全局渐近稳定的充分条件.     

Finite‐Time Stability and Stabilization of Linear Itô Stochastic Systems with State and Control‐Dependent Noise

In this paper, finite‐time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite‐time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite‐time stochastically stable are given. Subsequently, the finite‐time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite‐time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results.     

关于Lurie型控制系统的鲁棒绝对稳定性

用Lyapunov函数法研究了区间Lurie型间接控制系统与直接控制系统的鲁棒绝对 稳定性,给出了系统鲁棒绝对稳定的充分条件.一个应用实例说明该方法的优越性.