基于MDADT方法的离散切换系统L_2增益分析

An MDADT-Based approach for L_2-gain analysis of discretetime switched systems

主要研究一类离散时间的线性切换系统的稳定性和L_2增益问题,将应用一种模式依赖平均驻留时间(MDADT)的方法来分析这类离散时间线性切换系统的L_2增益属性。模式依赖平均驻留时间是指在系统每个切换模式下都有自己的平均驻留时间,这使得驻留时间与系统的模式相关。因此,旨在找到一个准确的可容许的切换信号下的MDADT值,使得整个系统是稳定的。利用多Lyapunov函数方法得到系统稳定及L_2增益属性的充分条件,该条件是典型的线性矩阵不等式,可用LMIs直接来求解。MDADT方法的引入,使得驻留时间小于一般情况下的平均驻留时间,从而使得系统全局一致指数稳定的条件具有更少的保守性。

In this article,we study the stability and the L2 gain analysis problem for a class of discrete-time switched linear systems.A mode-dependent average dwell time（MDADT）approach is applied to analyze the L2 gain performance for these discrete-time switched linear systems.The proposed switching law is the average dwell time（ADT）switching in that each mode in the underlying system has its own ADT.Therefore,in this article,we aim at finding a more general MDADT such that a set of admissible switched signals can be found and the underlying system is stable.Taking advantage of multiple Lyapunov functional method,a sufficient condition is obtained to guarantee the globally uniformly exponentially stable（GUES）with the L2 gain performance for the underlying systems.The condition is a typical linear matrix inequality,we can use LMIs to solve it;because MDADT is less than the commonly average time,a less conservative result is presented with this approach.