Stability and Stabilization of Block-cascading Switched Linear Systems  

作　　者：Ya-Hong Zhu Dai-Zhang Cheng 

出　　处：《International Journal of Automation and computing》2006年第4期404-413,共10页国际自动化与计算杂志（英文版）

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

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.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.

关 键 词：Switching linear system quadratic stability common quadratic Lyapunov function reducible Lie algebra cascading Quaker Lemma 

分 类 号：TP[自动化与计算机技术]