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Stabilization of a class of switched nonlinear systems

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Abstract

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes-Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.

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Authors and Affiliations

  1. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Daizhan Cheng & Zairong Xi

  2. Department of Manufacturing Engineering and Engineering Management, City University of HongKong, HongKong, China

    Gang Feng

Authors
  1. Daizhan Cheng
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  2. Gang Feng
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  3. Zairong Xi
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Additional information

This work is partly supported by the National Natural Science Foundation of China (No. 60274010, 60221301, 60334040, 60228003).

Daizhan CHENG received Ph.D. degree from Washington University, MO, in 1985. Since 1990, he is a professor with the Institute of Systems Science. Chinese Academy of Sciences. He was an Associate Editor of Math Sys., Est. Contr. (91–93), Automatica (98-02), Asia J. Control. (2001–2003). Deputy Chief Editor of Control and Decision, J. Control Theory and App. etc. Since 2003 he has been Chairman of the Technical Committee on Control Theory, Chinese Automation Association. He is the author/co-author of over 150 journal papers and 5 books. His research interests include nonlinear systems and control, Numerical Method. He is elected IEEE Fellow in 2005.

Gang FENG received the B.E. and M.E. degrees in Automatic Control (of Electrical Engineering) from Nanjing Aeronautical Institute, China in 1982 and in 1984 respectively, and the Ph.D. degree in Electrical Engineering from the University of Melbourne, Australia in 1992. He has been with City University of Hong Kong since 2000 and was with School of Electrical Engineering, University of New South Wales, Australia, 1992–1999. He was awarded an Alexander von Humboldt Fellowship in 1997–1998. He was a visiting Fellow at National University of Singapore (1997), and Aachen Technology University, Germany (1997–1998). He has authored and/or coauthored more than 100 referred international journal papers and numerous conference papers. His current research interests include robust adaptive control, signal processing, piecewise linear systems, and intelligent systems and control. Dr. Feng is an associate editor of IEEE Trans. on Fuzzy Systems, and IEEE Trans. on Systems, Man & Cybernetics, Part C, Journal, of Control Theory and Applications, and was an associate editor of the Conference Editorial Board of IEEE Control System Society.

Zairong XI was born in Hunan, China, in 1969. He received the M.S. degree in mathematics from Zhengzhou University, Zhengzhou, China, in 1997, and the Ph.D. degree in control theory from the Chinese Academy of Sciences, Beijing, China, in 2000. He was a Post-doctoral Fellow in Tsinghua University, Beijing. In 2002, he joined the Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Now he is Associate Professor. His research interests include nonlinear systems analysis and synthesis, power systems control, mechanical systems, stability analysis, robust control, and quantum control.

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Cheng, D., Feng, G. & Xi, Z. Stabilization of a class of switched nonlinear systems. J. Control Theory Appl. 4, 53–61 (2006). https://doi.org/10.1007/s11768-006-5259-0

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  • DOI: https://doi.org/10.1007/s11768-006-5259-0

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