This paper addresses robust 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 only by employing state-dependent switching rules. Then the robust 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 -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.
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September 2006
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Robust Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach
Zhijian Ji,
Zhijian Ji
School of Automation Engineering,
e-mail: jizhijian@pku.org.cn
Qingdao University
, Qingdao, Shandong, 266071, China
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Xiaoxia Guo,
Xiaoxia Guo
Department of Mathematics,
Ocean University of China
, 266071, China
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Long Wang,
Long Wang
Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science,
Peking University
, Beijing, China
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Guangming Xie
Guangming Xie
Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science,
Peking University
, Beijing, China
Search for other works by this author on:
Zhijian Ji
School of Automation Engineering,
Qingdao University
, Qingdao, Shandong, 266071, Chinae-mail: jizhijian@pku.org.cn
Xiaoxia Guo
Department of Mathematics,
Ocean University of China
, 266071, China
Long Wang
Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science,
Peking University
, Beijing, China
Guangming Xie
Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science,
Peking University
, Beijing, ChinaJ. Dyn. Sys., Meas., Control. Sep 2006, 128(3): 696-700 (5 pages)
Published Online: July 3, 2005
Article history
Received:
June 14, 2004
Revised:
July 3, 2005
Citation
Ji, Z., Guo, X., Wang, L., and Xie, G. (July 3, 2005). "Robust Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach." ASME. J. Dyn. Sys., Meas., Control. September 2006; 128(3): 696–700. https://doi.org/10.1115/1.2238874
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