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Asymptotic stability in pth moment of uncertain dynamical systems with time-delays

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  • Lu, Ziqiang
  • Zhu, Yuanguo

Abstract

Time-delay is a universal phenomenon in control systems, which usually leads to instability and poor performance of systems. In this paper, the pth moment asymptotic stability of trivial solutions to uncertain dynamical systems with time-delays is investigated. The concept of the generalized expected value is introduced with its properties based on uncertainty theory. Sufficient conditions for ensuring the stability of uncertain delay systems are derived by Lyapunov direct method. Several illustrative examples with numerical simulations are arranged to demonstrate the effectiveness of the stability results.

Suggested Citation

  • Lu, Ziqiang & Zhu, Yuanguo, 2023. "Asymptotic stability in pth moment of uncertain dynamical systems with time-delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 323-335.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:323-335
    DOI: 10.1016/j.matcom.2023.05.005
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    References listed on IDEAS

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    1. Wang, Xiao & Ning, Yufu & Peng, Zhen, 2020. "Some results about uncertain differential equations with time-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    2. Jia, Lifen & Sheng, Yuhong, 2019. "Stability in distribution for uncertain delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 49-56.
    3. Hu, Lunhu & Kang, Rui & Pan, Xing & Zuo, Dujun, 2020. "Risk assessment of uncertain random system—Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    4. Zhiyong Huang & Chunliu Zhu & Jinwu Gao, 2021. "Stability analysis for uncertain differential equation by Lyapunov’s second method," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 129-144, March.
    5. Wang, Xiao & Ning, Yufu & Moughal, Tauqir A. & Chen, Xiumei, 2015. "Adams–Simpson method for solving uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 209-219.
    6. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    7. Ziqiang Lu & Yuanguo Zhu & Qinyun Lu, 2021. "Stability Analysis Of Nonlinear Uncertain Fractional Differential Equations With Caputo Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-10, May.
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    Cited by:

    1. Arunagirinathan, S. & Lee, T.H., 2024. "Generalized delay-dependent reciprocally convex inequality on stability for neural networks with time-varying delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 109-120.

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