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A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay

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Listed:
  • Zhang, Dian
  • Cheng, Jun
  • Ki Ahn, Choon
  • Ni, Hongjie

Abstract

This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.

Suggested Citation

  • Zhang, Dian & Cheng, Jun & Ki Ahn, Choon & Ni, Hongjie, 2019. "A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 191-205.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:191-205
    DOI: 10.1016/j.amc.2018.09.035
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    References listed on IDEAS

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    1. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
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    4. Guo, Runan & Zhang, Ziye & Liu, Xiaoping & Lin, Chong, 2017. "Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 100-117.
    5. Wang, Bo & Yan, Juan & Cheng, Jun & Zhong, Shouming, 2017. "New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 322-333.
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    Cited by:

    1. Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Zhang, Dian & Cheng, Jun & Cao, Jinde & Zhang, Dan, 2019. "Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties," Applied Mathematics and Computation, Elsevier, vol. 344, pages 230-242.
    3. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    4. Lin, Yuqian & Zhuang, Guangming & Sun, Wei & Zhao, Junsheng & Chu, Yuming, 2021. "Resilient H∞ dynamic output feedback controller design for USJSs with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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