具有结构不确定性的输出反馈性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

稳定性切换点法在时滞系统的鲁棒稳定性中的应用

讨论了一类参数与时滞相关的时滞系统的鲁棒稳定性.在"稳定性切换几何判据法"的基础上提出了"稳定性切换点法",使用该方法可得到相应方程零解稳定的参数变化区域.针对向日葵方程这一实际例子,利用文中所提出的方法并结合Maple软件作图可以容易地得到稳定性区域和不稳定性区域以及两区域的分界线、Hopf分岔点等;进一步通过对时滞...     

具有结构不确定性的输出反馈线性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

多变量时滞系统鲁棒稳定性

基于Smith预估技术和多变量线性系统解耦鲁棒理论,研究了多变量时滞系统鲁棒 稳定性,得到在Smith预估严格匹配时闭环系统稳定,且摄动系统为鲁棒对角优势,则摄动系 统为鲁棒稳定的一般性结论.     

一类带有时滞的不确定广义系统的切换渐近稳定性

研究了一类带有时滞的切换不确定广义系统的鲁棒渐近稳定问题. 利用Lyapunov稳定性定理和线性矩阵不等式(Linear matrix inequality, LMI)工具, 采用多Lyapunov函数技术, 在设定的切换律下, 得到切换不确定广义时滞系统鲁棒渐近稳定的时滞相关充分条件. 进一步, 建立了一个具有线性矩阵不等式约束的凸优化问题, 利用Matlab软件中的LMI工具箱求解, 得到保证切换广义系统鲁棒渐近稳定的最大可允许时滞上界. 最后示例表明了该方法的有效性.     

基于互质因子摄动的反馈系统的鲁棒稳定性

考虑对象和控制器同时具有互质因子摄动时闭环系统的鲁棒稳定性问题,得到了闭环 系统鲁棒稳定的充要条件并给出了鲁棒控制器的优化设计方法.     

一类不确定随机切换系统的镇定性和H∞性能研究

针对一类不确定随机切换系统,利用随机李亚普诺大稳定性理论和伊藤微分法则,研究了该系统在一定切换条件下鲁棒镇定和鲁棒H∞控制器存在的充分条件.使用状态反馈技术所设计的无记忆控制器能在所有容许不确定下保证闭环系统渐近稳定.文中的研究结果以线性矩阵不等式的形式给出,算例和仿真表明文中控制器设计方法的正确性和有效性.     

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.     

线性时变系统的区间稳定性与鲁棒稳定性

本文应用向量比较定理研究线性时变系统的区间稳定性和具非线性时变摄动的线性时变系统的鲁棒稳定性，所得的新结果包含文献的一些主要结果作为特例，本文的研究方法说明向量比较方法是分析区间稳定性和鲁棒稳定性的一种自然而有力的工具。     

时滞线性系统的与时滞无关稳定性

本文利用结构奇异值概念讨论时滞线性系统的与时滞无关之渐近稳定性。本文结果表明时滞可看成某一“标称”系统的重复标量不确定摄动快。当系统具其它结构摄动时，鲁棒稳定分析可在结构奇异值方法框架上进行。     

短时延多包传输网络控制系统的稳定性分析

提出一种短时延多包传输网络控制系统的建模方法.把多包传输网络控制系统建模为具有一定切换规则的线性切换系统模型.利用切换系统理论和鲁棒稳定性理论，得到多包传输网络控制系统的渐近稳定性判据,并首次提出周期动态输出反馈镇定控制器的设计方法.最后通过数值算例证明文中结论的可行性和有效性.     

Exponential Stability and Asynchronous Stabilization of Switched Systems With Stable and Unstable Subsystems

This paper deals with the exponential stability and asynchronous stabilization of continuous‐time switched systems. By delicately constructed piecewise Lyapunov‐like functions and the minimum dwell time switching method, exponential stability of the switched systems with stable or unstable subsystems is obtained. Based on the result of the stability, the problem of controller design of the switched systems under asynchronous switching is also solved, and the delay that causes asynchronous phenomena can be unbounded. The stability results and control laws of the switched systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results.     

Stability analysis and control synthesis of switched impulsive systems

In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems of switched discrete‐time linear systems are studied. First, sufficient conditions ensuring globally uniformly asymptotically stability of switched nonlinear impulsive system under arbitrary and DDT (dynamical dwell time which defines the length of the time interval between two successive switchings) switching are derived, respectively. In the DDT switching case, we first consider the switched system composed by stable subsystems, then we extend the results to the case where not all subsystems are stable. The stabilizations of switched discrete‐time linear system under arbitrary switching, DDT switching and asynchronous switching are investigated respectively. Based on the stability analysis results, the control synthesis consists of controller design for each subsystem and state impulsive jumping generators design at switching instant. With the aid of the state impulsive jumping generators at switching instant, the ‘energy’ produced by switching can be minimized, which leads to less conservative results. Several numerical examples are given to illustrate the proposed results within this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability and stabilization of switched stochastic systems under asynchronous switching

This paper studies the stability and stabilization problems for a class of switched stochastic systems under asynchronous switching. The asynchronous switching refers to that the switching of the candidate controllers does not coincide with the switching of system modes. Two situations are considered: (1) time-delayed switching situation, that is, the switching of the candidate controllers has a lag to the switching of the system modes; (2) mismatched switching situation, the switching of the candidate controllers does not match the switching of the system modes. Using average dwell time and Lyapunov-like function, sufficient conditions are established for stochastic input-to-state stability of the whole system. Also, the stabilizing controller design approach is proposed for switched stochastic linear systems. The minimal average dwell time and the controller gain are achieved. Finally, a numerical example is used to demonstrate the validity of the developed results.     

切换状态反馈控制系统的稳定性分析

研究了一类切换控制系统的稳定性分析问题,切换控制器由多个线性状态反馈控制器组成。运用Lyapunov方法得出了稳定性的时域判据,通过求解一个线性矩阵不等式的方法分析切换控制系统的稳定性,利用KYP引理得到了等价的频域判据;并且研究了一类含有参数不确定性的切换控制系统的鲁棒稳定性分析问题,给出了稳定性时域判据和频域判据。稳定性分析的主要结果是基于公共二次Lyapunov函数的,适用于切换系统任意切换的情形,该方法在工程实例中的应用表明了其有效性。     

Robust stability analysis of uncertain switched linear systems with unstable subsystems

The problem of robust stability for switched linear systems with all the subsystems being unstable is investigated. Unlike the most existing results in which each switching mode in the system is asymptotically stable, the subsystems may be unstable in this paper. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, sufficient conditions of exponential stability for both deterministic and uncertain switched linear systems are presented by using the invariant subspace theory and average dwell time method. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law. Several examples are included to show the effectiveness of the theoretical findings.     

一类切换线性系统的稳定性判别方法

研究了子系统中系统矩阵为对角标准型或者Jordan标准型的切换线性系统的稳定性．用状态方程的解来分析系统能量函数（状态向量的2范数）的单调性,得到系统在任意切换序列下渐近稳定的充分条件．另外,根据这些条件可以比较容易地设计出渐近稳定的切换序列．最后通过一个数值例子来说明所得到结论的效果．     

Stability analysis for uncertain switched neutral systems with discrete time-varying delay: A delay-dependent method

This paper considers the robust stability of a class of switched neutral systems with discrete time-varying delay and time-varying structure. Sufficient conditions for exponential stability criteria are developed for arbitrary switching signal with average dwell time. The results are obtained based on Lyapunov’s stability analysis via Krasovsky–Lyapunov’s functionals and the related stability study is performed to obtain delay-dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are exponentially stabile. These conditions are delay-dependent and are given in the form of linear matrix inequalities (LMIs). Some examples are worked out to illustrate the effectiveness of the result.     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

Analysis of robust stability for switched systems with multiple time-delays

The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method.The interaction between different time-delays is considered.The sufficient conditions do not need that every subsystem is stable.The designed methods of the switching law are also given.The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily.The result is proven to be valid by the simulation at last.