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Learning-based asynchronous sliding mode control for semi-Markov jump systems with time-varying delay using relaxed negative-determination lemma

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  • Han, Lihuan
  • Ma, Yuechao

Abstract

This article figures out the asynchronous sliding mode control (SMC) issue for a class of semi-Markov jump systems (SMJSs) with time-varying delay and actuator faults. Firstly, to tackle the chattering produced by asynchronous phenomenon and guarantee smooth reachability, the hidden Markov model and the reduced-order theory are used to design the learning-based SMC law. Besides, the mode-dependent augmented Lyapunov–Krasovskii functional (LKF) is constructed. By using the relaxed negative definite lemma and the generalized free matrix integral inequality (GFMBII), sufficient conditions for ensuring the stochastic stability of the SMJSs are provided. Furthermore, the conservatism of the maximum time delay is effectively reduced by adjusting the value of β. Finally, simulation examples prove the validity and superiority of the proposed method.

Suggested Citation

  • Han, Lihuan & Ma, Yuechao, 2024. "Learning-based asynchronous sliding mode control for semi-Markov jump systems with time-varying delay using relaxed negative-determination lemma," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077924000055
    DOI: 10.1016/j.chaos.2024.114454
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    References listed on IDEAS

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    1. Zhao, Wenying & Ma, Yuechao & Chen, Aihong & Fu, Lei & Zhang, Yutong, 2019. "Robust sliding mode control for Markovian jump singular systems with randomly changing structure," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 81-96.
    2. Tao, Ruifeng & Ma, Yuechao & Wang, Chunjiao, 2020. "Stochastic admissibility of singular Markov jump systems with time-delay via sliding mode approach," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    3. Cao, Qian & Wei, Du Qu, 2023. "Dynamic surface sliding mode control of chaos in the fourth-order power system," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. 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.
    5. Wang, Xingxing & Ma, Yuechao, 2023. "Adaptive non-fragile sliding mode control for switched semi-Markov jump system with time-delay and attack via reduced-order method," Applied Mathematics and Computation, Elsevier, vol. 440(C).
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    Cited by:

    1. Liu, Li-Juan & Chen, Shu-Yue & Karimi, Hamid Reza & Zhang, Zhao, 2024. "Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).

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