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Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System

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Abstract

Switching Markov jump linear system (SMJLS), a special hybrid system, has attracted a lot of studies recently. SMJLS is governed by stochastic and deterministic commutations. This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems. Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided, and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities (LMIs). Finally, numerical examples are given to show the feasibility and effectiveness of the results.

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Authors and Affiliations

  1. Department of Automation, School of Mechatronics Engineering and Automation, Shanghai University, Shanghai, 200444, China

    Yunyun Jin  (靳云云), Yang Song  (宋杨) & Yongzhuang Liu  (刘永壮)

  2. Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai, 200444, China

    Yang Song  (宋杨)

  3. School of Information Engineering, Zhengzhou University, Zhengzhou, 450001, China

    Weiyan Hou  (侯维岩)

Authors
  1. Yunyun Jin  (靳云云)
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  2. Yang Song  (宋杨)
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  3. Yongzhuang Liu  (刘永壮)
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  4. Weiyan Hou  (侯维岩)
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Corresponding author

Correspondence to Yang Song  (宋杨).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 61573237), the “111 Project” (No. D18003), and the Program of China Scholarship Council (No. 201906895021)

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Jin, Y., Song, Y., Liu, Y. et al. Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System. J. Shanghai Jiaotong Univ. (Sci.) 25, 674–680 (2020). https://doi.org/10.1007/s12204-020-2205-0

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  • DOI: https://doi.org/10.1007/s12204-020-2205-0

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