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Stability of a class of switched stochastic nonlinear systems under asynchronous switching

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  • Control Theory
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Abstract

The stability of a class of switched stochastic nonlinear retarded systems with asynchronous switching controller is investigated. By constructing a virtual switching signal and using the average dwell time approach incorporated with Razumikhin-type theorem, the sufficient criteria for pth moment exponential stability and global asymptotic stability in probability are given. It is shown that the stability of the asynchronous stochastic systems can be guaranteed provided that the average dwell time is sufficiently large and the mismatched time between the controller and the systems is sufficiently small. This result is then applied to a class of switched stochastic nonlinear delay systems where the controller is designed with both state and switching delays. A numerical example illustrates the effectiveness of the obtained results.

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Author information

Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, China

    Dihua Zhai & Yu Kang

  2. School of Electrical Engineering, University of Jinan, Jinan, China

    Ping Zhao

  3. Department of Chemical Engineering, Imperial College London, London, UK

    Yun-Bo Zhao

  4. CTGT centre, Harbin Institute of Technology, Harbin, China

    Yun-Bo Zhao

Authors
  1. Dihua Zhai
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  2. Yu Kang
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  3. Ping Zhao
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  4. Yun-Bo Zhao
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Corresponding author

Correspondence to Yu Kang.

Additional information

Recommended by Editor Ju Hyun Park.

This journal was supported in part by the National Natural Science Foundation of P. R. China under grant No.60935001, 61174061, 60904024, 60934006, the Anhui Provincial Natural Science Foundation (11040606M143), the Doctoral Foundation of University of Jinan (XBS1012), the Fundamental Research Funds for the Central Universities, the Program for New Century Excellent Talents in University, and the Program for Youth Innovation Promotion Association, CAS.

Dihua Zhai received his B.S. degree in Automation from the Anhui University, P. R. China, in 2010. He is currently a M.S. student in the Department of Automation, University of Science and Technology of China, P. R. China. His research interests are in the stability theory and control of switched systems, networked control systems and stochastic systems, etc.

Yu Kang received his Dr. Eng. degree in Control Theory and Control Engineering, University of Science and Technology of China, P. R. China, in 2005. From 2005 to 2007, he was a postdoctoral fellow in the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. R. China. Currently, he is an Associate Professor in the Department of Automation, University of Science and Technology of China, China. Dr. Kang’s current research interests are in the adaptive/robust control, variable structure control, mobile manipulator, Markovian jump systems, etc.

Ping Zhao received his B.S. degree from the University of Jinan, P. R. China, in 2002, an M.S. degree from the Qufu Normal University, P. R. China, in 2005, and a Ph.D. from Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He is currently a teacher of University of Jinan. His research interests are in the stability theory and control of stochastic and nonlinear systems.

Yun-Bo Zhao received his B.Sc. degree in Mathematics from Shandong University, Shandong, P. R. China, in 2003, an M.Sc. degree in Systems Theory from the Institute of Systems Science, Chinese Academy of Sciences, Beijing, P. R. China, in 2007, and a Ph.D. degree from the University of Glamorgan, Pontypridd, U.K., in 2008. He is currently a Research Associate with Imperial College London, London, U.K. His research interests include systems biology, networked control systems, and Boolean networks.

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Zhai, D., Kang, Y., Zhao, P. et al. Stability of a class of switched stochastic nonlinear systems under asynchronous switching. Int. J. Control Autom. Syst. 10, 1182–1192 (2012). https://doi.org/10.1007/s12555-012-0613-0

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