带有混合时滞的切换系统的耗散性分析与控制

Dissipative analysis and control of switched systems with mixed time delays

中文关键词  耗散控制  切换系统  混合时变时滞  模态依赖平均驻留时间  Lyapunov-Krasovskii泛函

英文关键词  dissipative control  switching system  mixed time-varying delays  mode-dependent average dwell time  Lyapunov-Krasovskii functional

中文摘要

      本文研究了一类具有不稳定子系统和混合时滞的切换系统的耗散性和指数镇定问题. 首先, 为了消除不稳 定子系统给这类时滞系统带来的不利影响, 采用了一种新颖的切换信号设计方法–将模态依赖平均驻留时间的慢切 换和快切换方法相结合, 并通过利用Lyapunov相关理论, 给出了全局指数稳定的充分条件. 然后, 利用耗散性理 论、多重Lyapunov-Krasovskii泛函技术、积分不等式、与Schur补引理等方法, 以线性矩阵不等式的形式给出了耗散 性能的相关判据, 使闭环系统实现全局指数稳定性的同时具有严格耗散性能. 进一步, 在给定扰动衰减水平的前提 下, 通过求解一些严格的LMI条件, 建立了一组可行控制器. 最后, 通过仿真实例验证了该方法的有效性.

英文摘要

      This paper deals with the problems of dissipativity and exponential stabilization for switched systems with unstable subsystems and mixed time delays. First, in order to eliminate the adverse effects of unstable subsystems on such time-delay systems, a novel switching signal design method is adopted in this paper, which combines slow switching and fast switching with the mode-dependent average dwell time technique. And by using Lyapunov theory, sufficient conditions for global exponential stability of closed-loop systems are given. Then, delay-dependent criteria are derived in terms of linear matrix inequalities by employing dissipativity theory, multiple Lyapunov-Krasovskii functional approaches, mode-dependent average dwell time technique and Jensen’s integral inequality, making the closed-loop system achieve exponential stability and strict dissipativity. In addition, with the given premise of disturbance attenuation level, a set of feasible controllers are established by solving some strict LMI conditions. Finally, a simulation example is given to demonstrate the availability of the acquired methods.