Quadratic stabilization of switched systems

Abstract

Abstract We consider quadratic stabilization of uncertain switched systems when a switching rule is imposed on state feedback controllers of subsystems. A method is proposed to constructively design switching rules for continuous and discrete-time switched systems with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched system is quadratically stabilizable via switched state feedback for all uncertainties. Keywords: Uncertain switched systemsQuadratic stabilityLyapunov methodFeedback stabilizationSwitching rule Acknowledgements The authors would like to thank Professor Fleming and the three reviewers for their constructive and insightful suggestions for further improving the quality and presentation of this paper. This work is supported by National Natural Science Foundation of China (No. 10372002, No. 60274001, No. 60404001) and National Key Basic Research and Development Program (2002CB312200). Zhijian Ji received the MS degree in Applied Mathematics from Ocean University of China in 1998. He is currently a PhD student in the Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China. From 1998 to 2002, he was with Qingdao University as an associate professor. His current research interests are in the fields of nonlinear control systems, switched and hybrid systems. He was the winner of the first-class scholarship of China Petrol in 2003, the Innovation Award and the May Fourth Scholarship of Peking University in 2004. E-mail: jizhijian@pku.edu.cn Long Wang was born in Xian, China on 13 February 1964. He received his Bachelor, Master, and Doctor's degrees in Dynamics and Control from Tsinghua University and Peking University in 1986, 1989, and 1992, respectively. He has held research positions at the University of Toronto, Canada, and the German Aerospace Center, Munich, Germany. He is currently Cheung Kong Chair Professor of Dynamics and Control and Director of Center for Systems and Control of Peking University. He is also Vice-Director of National Key Laboratory of Complex Systems and Turbulence. He is a panel member of the Division of Information Science, National Natural Science Foundation of China. He is on the editorial boards of Progress in Natural Science, Acta Automatica Sinica, Journal of Control Theory and Applications, Control and Decision, Information and Control, etc. His research interests are in the fields of networked systems, hybrid systems, swarm dynamics, cognitive science, collective intelligence, and bio-mimetic robotics. E-mail: longwang@pku.edu.cn Guangming Xie received the BS degree in Applied Mathematics and Computer Science & Technology, the ME degree in Control Theory and Control Engineering, and the PhD degree in Control Theory and Control Engineering from Tsinghua University, Beijing, China in 1996, 1998, 2001, respectively. He then worked as a postdoctoral research fellow in the Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China from July 2001 to June 2003. He is currently a lecturer in the Center for Systems and Control, Peking University. His research interests include hybrid and switched systems, networked control systems, multi-agent systems, multi-robot systems and swarm intelligence.