时滞不确定性Markov切换线性随机微分系统的指数鲁棒稳定性

研究了一类时滞不确定性Markov切换随机微分系统的均方指数鲁棒随机稳定性\bd 系统中的时滞是时变的, 不确定项结构为范数有界, Markov切换是连续时间、离散状态的时齐Markov过程{\bf\!.} 利用随机Lyapunov函数方法和LMI技术, 得到了几个判定系统均方指数鲁棒随机稳定性的充分性条件\bd 一个数值例子说明了判据的有效性和可行性.     

含非线性项的不确定离散时滞系统鲁棒稳定性分析

针对一类同时存在非线性项和不确定项的离散时滞系统,研究了系统的鲁棒稳定性问题.通过构造Lyapunov函数并利用Schur补引理以线性矩阵不等式(LMI)形式给出了系统鲁棒稳定的充分条件;利用离散时滞系统鲁棒稳定性的充分条件,采用LMI技术,设计出基于LMI的状态反馈鲁棒控制器;理论证明该方法设计的控制器保证闭环系统鲁棒渐近稳定.     

非线性离散开关系统的鲁棒镇定问题

利用切换Lypunov函数方法,把非线性离散开关系统的鲁棒镇定问题转化成一个矩阵不等式的最优解问题,给出了在任意切换下具有非线性扰动的线性开关系统的可鲁棒镇定的充分条件,并进一步讨论了同类时滞开关系统的鲁棒镇定问提.最后把以上结论推广到广义开关系统,由于结果均以矩阵不等式形式给出,便于验证和实现.     

不确定时滞Lurie系统的鲁棒绝对稳定性分析

研究了一类不确定Lurie时滞系统的鲁棒绝对稳定性问题，不确定项范数有界。通过构造特殊的李亚普诺夫函数，分别考虑了时滞相关和时滞无关两情况，得到了系统鲁棒绝对稳定的充分条件。     

具有时变灰参数的随机时滞系统的p-阶矩指数鲁棒稳定性

利用灰矩阵的矩阵覆盖集的分解技术和Lyapunov函数法,研究了具有时变灰色参数的随机时滞系统的p-阶矩指数鲁棒稳定性问题,得到了该系统p-阶矩指数鲁棒稳定的时滞独立和时滞依赖的条件,并通过数值例子说明了判别条件的有效性和实用性.     

灰色中立随机线性时滞系统的稳定性分析(英文)

通过使用灰色矩阵覆盖集的分解方法和矩阵范数的性质,构造李雅普诺夫函数,研究了灰色中立随机线性时滞系统的鲁棒稳定性和几乎指数鲁棒稳定性.     

具有非线性扰动的线性多时变时滞系统的鲁棒稳定性

采用了一类新型积分等式,研究了具有非线性扰动的线性多时变时滞系统的时滞相关鲁棒稳定性问题,并推广得到一般的时滞相关－时滞变化率无关的鲁棒稳定性条件.数值实例表明,稳定性条件的保守性也有所减少.     

时滞切换神经网络系统的鲁棒指数稳定性

研究了具有时间滞后切换不确定细胞神经网络(UCNNs)系统的指数稳定性.利用同胚映射和M矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用平均驻留时间方法,研究了时滞切换UCNNs系统限制切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

两类时滞系统的鲁棒性分析

考虑了两类具有参数不确定性的时滞系统的鲁棒稳定性问题, 给出了系统具有鲁棒性能的几个充要条件. 这些结论对于研究具有时滞的反馈控制系统有重要的理论和实践价值.     

一类不确定线性切换系统二次鲁棒稳定性的充分条件

本文研究了一类不确定线性切换系统的二次鲁棒稳定性问题.首先利用矩阵集的严格完备性设计切换律,导出了二次鲁棒稳定的充分条件.同时得到了在任意切换策略下,当矩阵集的所有矩阵为负定时保证切换系统二次鲁棒稳定性.在适当的假设下,这些条件可以表示为矩阵不等式.最后,用数值例子对所得结果加以阐明,说明了文中结果的正确性.     

A geometric approach for reachability and observability of linear switched impulsive systems

This paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices. First some new concepts with respect to the reachability and unobservability are introduced. Especially, span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces. Then the geometric characterization of the span reachable and unobservable sets is presented. Moreover, the relations between the span reachable set, unobservable set and the invariant subspaces of such systems are discussed. Finally, corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed.     

Stabilization for switched nonlinear time-delay systems

This paper investigates the problem of stabilization for a class of switched nonlinear systems with time-delay. Based on the differential mean value theorem (DMVT), the switched nonlinear systems are transformed into switched linear parameter varying (LPV) systems. By using multiple Lyapunov function approach and convexity principle, and via observer-based output feedback, a sufficient condition for the stabilization of the original system is proposed, which has been expressed in terms of linear matrix inequalities (LMIs). Further, the control method is extended to a class of switched nonlinear systems with norm-bounded uncertainties. A new sufficient condition is proposed, which guarantees the class of uncertain switched systems, is asymptotically stabilizable. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.     

Stability analysis and uniform ultimate boundedness control synthesis for a class of nonlinear switched difference systems

In this paper, we deal with stability analysis of a class of nonlinear switched discrete-time systems. Systems of the class appear in numerical simulation of continuous-time switched systems. Some linear matrix inequality type stability conditions, based on the common Lyapunov function approach, are obtained. It is shown that under these conditions the system remains stable for any switching law. The obtained results are applied to the analysis of dynamics of a discrete-time switched population model. Finally, a continuous state feedback control is proposed that guarantees the uniform ultimate boundedness of switched systems with uncertain nonlinearity and parameters.     

Stability of switched systems with time delay

In this paper, we study the qualitative properties of linear and nonlinear delay switched systems which have stable and unstable subsystems. First, we prove some inequalities which lead to the switching laws that guarantee: (a) the global exponential stability to linear switched delay systems with stable and unstable subsystems; (b) the local exponential stability of nonlinear switched delay systems with stable and unstable subsystems. In addition, these switching laws indicate that if the total activation time ratio among the stable subsystems, unstable subsystems and time delay is larger than a certain number, the switched systems are exponentially stable for any switching signals under these laws. Some examples are given to illustrate the main results.     

Stability analysis of switched impulsive systems with time delays

In this paper, a new stability analysis of switched impulsive systems with time delays whose subsystem is not necessarily stable is presented. A sufficient condition on uniformly asymptotical stability for nonlinear switched impulsive systems is obtained. Using the result obtained and the minimum (maximum) holding time, an easily verifiable condition on uniformly asymptotical stability for linear switched impulsive systems with time delays is derived. The control synthesis is also discussed. Finally, two examples with simulation results are given to validate the results.     

A Switching Law to Stabilize an Unstable Switched Linear System

Stabilization of switched systems fully composed of unstable modes is of theoretical and practical significance. In this paper, we obtain some sufficient algebraic conditions for stabilizing switched linear systems with all unstable subsystems based on the theory of spherical covering and crystal point groups. Under the proposed algebraic conditions switching laws are easy to be designed to stabilize the switched systems. Some simple examples are provided to illustrate our results.     

Periodical stabilization of switched linear systems

Periodical stabilization problems for switched linear systems are investigated in this paper. For autonomous switched systems, if there exists a stable convex combination of the subsystems, then a periodically switching signal can be constructed such that the overall system is asymptotically stable. Based on this fact, for switched control systems, corresponding sufficient conditions are presented under which constant/switching direct/observer-based state feedback controller can be designed such that the corresponding closed-loop systems are asymptotically stable under some periodically switching signal. Some numerical examples are given to illustrate our results.     

Equivalence of several characteristics of dual switched linear systems

This paper is concerned with the equivalence of several dynamic characteristics between mutually dual switched linear systems, both discrete- and continuous-time cases are considered. Two systems are mutually dual means that their system matrices are transpose of each other. The dynamic properties considered in this paper include four types: exponential stability, global uniform asymptotic stability, attractivity, and weak attractivity. It is shown that every one of the four dynamic properties of a switched linear system implies each of the four dynamic properties of its dual system, and vice versa. The main results enable us to investigate these dynamic properties of switched system by virtue of study related to the corresponding properties of its dual system, thus providing an alternative way to explore the dynamics of switched systems. A numerical example is provided to illustrate the obtained theoretical conclusions.     

Quadratic stabilization of a class of switched nonlinear systems via single Lyapunov function

This paper is concerned with the problem of globally quadratic stabilization for a class of switched cascade systems. The system under consideration is composed of two subsystems: a linear switched part and a nonlinear part, which are also switched systems. The feedback control law and the switching law are designed respectively when the first part is stabilized under some switching law and when both parts can be stabilized under some switching laws. We construct the single Lyapunov functions and design the switching laws based on the structure characteristics of the switched system. Also, the designed switching laws are of hysteresis switching form in order to avoid sliding models.