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Robust H Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

[+] Author and Article Information
Zhijian Ji

School of Automation Engineering, Qingdao University, Qingdao, Shandong, 266071, Chinajizhijian@pku.org.cn

Xiaoxia Guo

Department of Mathematics, Ocean University of China, 266071, China

Long Wang, Guangming Xie

Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China

J. Dyn. Sys., Meas., Control 128(3), 696-700 (Jul 03, 2005) (5 pages) doi:10.1115/1.2238874 History: Received June 14, 2004; Revised July 03, 2005

This paper addresses robust H control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

Copyright © 2006 by American Society of Mechanical Engineers
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