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On the stabilization of switched linear stochastic systems with unobservable switching laws

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Abstract

This paper is concerned with the stabilization problem of switched linear stochastic systems with unobservable switching laws. In this paper the system switches among a finite family of linear stochastic systems. Since there are noise perturbations, the switching laws can not be identified in any finite time horizon. We prove that if each individual subsystem is controllable and the switching duration uniformly has a strict positive lower bound, then the system can be stabilized by using a controller that uses online state estimation.

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Peng Ye & Haitao Fang

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  1. Peng Ye
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  2. Haitao Fang
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Additional information

This work was supported by the National Natural Science Foundation of China (No. 60274003, 60221301).

Peng YE was born in Anhui, China, in 1980. He received the B.S. degree in statistics and probability from the Peking University. Now he is pursuing his Master degree in the Key Laboratory of Systems and Control, Chinese Academy of Sciences. His current research interest is Stochastic Control Systems.

Haitao FANG received his B.S. degree in probability and statistics in 1990, M.S. degree in applied mathematics in 1993 and Ph.D. degree in 1996 respectively from the Peking University, Tsinghua University and Peking University. He now is with Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences as an Associate Professor. From 1996–1998 he was a postdoctoral research fellow at the Institute of Systems Science and joined the Institute as an Assistant Professor in 1998. During 1998–1999, 2001, he was with Hong Kong University of Science and Technology as a Research Associate. His current research interests include stochastic optimization and systems control, communication systems, signal processing.

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Ye, P., Fang, H. On the stabilization of switched linear stochastic systems with unobservable switching laws. J. Control Theory Appl. 4, 44–52 (2006). https://doi.org/10.1007/s11768-006-4248-7

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  • DOI: https://doi.org/10.1007/s11768-006-4248-7

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