Stabilization of a Class of Switched Systems with Unstabilizable Switchin Modes

作     者：Zhu Yahong, Cheng Daizhan Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080 

会议名称：《第25届中国控制会议》

会议日期：2006年

学科分类：080804[工学-电力电子与电力传动] 0808[工学-电气工程] 08[工学] 

基　　金：This work is supported partly by NNSF  60221301  60334040 of China 

关 键 词：Switched control system Exponential stability Common quadratic Lyapunov function Lyapunov function with homogeneous derivative. 

摘      要：正This paper considers the stabilization of a class of switched control systems. Every switching mode is assumed to be not stabilizable. First, the linear case is considered. Assume the switching strategy and control are designable, a new stabilization technique is proposed, which stabilizes the unstabilizable sub-system by proper switching strategy and then stabilizes the stabilizable sub-system by using common quadratic Lyapunov function approach to the closed-loop sub-system. An easily verifiable sufficient condition is obtained. An illustrative example is provided to demonstrate the design procedure. Then using Lyapunov function with homogeneous derivative, similar design technique is used to stabilize switched nonlinear systems.