Stability and Stabilization of Block-cascading Switched Linear Systems

作     者：Ya-Hong Zhu Dai-Zhang Cheng 

作者机构：Institute of Systems Science Chinese Academy of Sciences Beijing PRC 

出 版 物：《International Journal of Automation and computing》 (国际自动化与计算杂志（英文版）)

年 卷 期：2006年第3卷第4期

页      面：404-413页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported partly by National Natural Science Foundation of PRC (No. 60343001  60274010  66221301 and 60334040) 

主　　题：Switching linear system quadratic stability common quadratic Lyapunov function reducible Lie algebra,cascading Quaker Lemma 

摘      要：The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.