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Finite-Time Asynchronous H ∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems

Author

Listed:
  • Qian Wang

    (School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Xiaojun Zhang

    (School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Yu Shao

    (School of Automation, Southeast University, Nanjing 210096, China)

  • Kaibo Shi

    (School of Information Science and Engineering, Chengdu University, Chengdu 610106, China)

Abstract

This article explores the finite-time control problem associated with a specific category of non-homogeneous hidden semi-Markov jump systems. Firstly, a hidden semi-Markov model is designed to characterize the asynchronous interactions that occur between the true system mode and the controller mode, and emission probabilities are used to establish relationships between system models and controller modes. Secondly, a novel piecewise homogeneous method is introduced to tackle the non-homogeneous issue by taking into account the time-dependent transition rates for the jump rules between different modes of the system. Thirdly, an asynchronous controller is developed by applying Lyapunov theory along with criteria for stochastic finite-time boundedness, ensuring the specified H ∞ performance level is maintained. Finally, the effectiveness of this method is verified through two simulation examples.

Suggested Citation

  • Qian Wang & Xiaojun Zhang & Yu Shao & Kaibo Shi, 2024. "Finite-Time Asynchronous H ∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems," Mathematics, MDPI, vol. 12(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3036-:d:1488142
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    References listed on IDEAS

    as
    1. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    2. Nguyen, Khanh Hieu & Kim, Sung Hyun, 2020. "Observer-based control design of semi-Markovian jump systems with uncertain probability intensities and mode-transition-dependent sojourn-time distribution," Applied Mathematics and Computation, Elsevier, vol. 372(C).
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