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Stabilization of Markov Jump Linear Systems with Input Quantization

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Abstract

This paper addresses the feedback stabilization problem for Markov jump linear systems with quantized control input. A simple but powerful input controller for eliminating the input quantization in Markov jump linear systems is used. The proposed mode-dependent input controller comprises two parts: the linear part and the nonlinear part, where the linear part determines the fundamental characteristics of the systems, and the nonlinear part eliminates the effect of the input quantization. The stability is analyzed in detail for both the discrete-time and continuous-time Markov jump linear systems with input quantization. The sufficient conditions and the specific mode-dependent input controller to guarantee the stability of the systems are obtained. Numerical examples are given to illustrate the effectiveness of the results.

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Acknowledgments

This paper is partly supported by the National Science Foundation of China (61025016, 61473183, 61034008, 61221003), Program of Shanghai Subject Chief Scientist(14XD1402400), and SJTU M&E Joint Research Foundation (YG2013MS04). The authors would like to extend the most sincere gratitude to the Associate Editor and the anonymous reviewers for their comments and suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Mingming Ji

  2. College of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Zhijun Li

  3. Department of Automation and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai Jiao Tong University, Shanghai, 200240, China

    Bo Yang & Weidong Zhang

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  1. Mingming Ji
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  2. Zhijun Li
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  3. Bo Yang
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  4. Weidong Zhang
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Correspondence to Weidong Zhang.

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Ji, M., Li, Z., Yang, B. et al. Stabilization of Markov Jump Linear Systems with Input Quantization. Circuits Syst Signal Process 34, 2109–2126 (2015). https://doi.org/10.1007/s00034-014-9959-2

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  • DOI: https://doi.org/10.1007/s00034-014-9959-2

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