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Event-based reachable set synthesis for delayed nonlinear semi-Markov systems

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  • Shen, Zhihao
  • Zhang, Liang
  • Niu, Ben
  • Zhao, Ning

Abstract

In this study, the issue of the reachable set (RS) synthesis for delayed nonlinear semi-Markov jump systems (s-MJSs) is addressed. An asynchronous controller whose controller mode is different from the system mode is designed. Non-fragile issues are considered in the design of the controller to improve the performance of the controller. Meanwhile, in order to economize on communication resources, the introduction of an event-triggered mechanism is considered in this work. A sufficient condition for the linear matrix inequalities (LMIs) form is obtained by utilizing the theory of Lyapunov functionals and the free-weighting matrix method, which ensures that the RS of the system is constrained by a compact ellipsoid. The controller gains of the system are then obtained by matrix decoupling. Ultimately, a numerical simulation and a practical model are provided to highlight the usability and practicality of the method.

Suggested Citation

  • Shen, Zhihao & Zhang, Liang & Niu, Ben & Zhao, Ning, 2023. "Event-based reachable set synthesis for delayed nonlinear semi-Markov systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011864
    DOI: 10.1016/j.chaos.2023.114284
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    References listed on IDEAS

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    1. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    2. Liu, Yan & Yu, Pinrui & Chu, Dianhui & Su, Huan, 2019. "Stationary distribution of stochastic Markov jump coupled systems based on graph theory," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 188-195.
    3. Feng, Zhiguang & Feng, Bo & Zhang, Naifu, 2023. "Fuzzy-based asynchronous controller design on reachable set synthesis of nonlinear hidden Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Zhang, Jianan & Ma, Yuechao, 2023. "Adaptive fault-tolerant double asynchronous control for switched semi-Markov jump systems via improved memory sampled-data technique," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
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    Cited by:

    1. Zhang, Liang & Liang, Jing & Feng, Zhiguang & Zhao, Ning, 2024. "Improved results of asynchronous mixed H∞ and passive control for discrete-time linear switched system with mode-dependent average dwell time," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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