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Stability analysis for uncertain differential equation by Lyapunov’s second method

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  • Zhiyong Huang

    (Renmin University of China)

  • Chunliu Zhu

    (Renmin University of China)

  • Jinwu Gao

    (Ocean University of China)

Abstract

Uncertain differential equation is a type of differential equation driven by Liu process that is the counterpart of Wiener process in the framework of uncertainty theory. The stability theory is of particular interest among the properties of the solutions to uncertain differential equations. In this paper, we introduce the Lyapunov’s second method to study stability in measure and asymptotic stability of uncertain differential equation. Different from the existing results, we present two sufficient conditions in sense of Lyapunov stability, where the strong Lipschitz condition of the drift is no longer indispensable. Finally, illustrative examples are examined to certify the effectiveness of our theoretical findings.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:20:y:2021:i:1:d:10.1007_s10700-020-09336-7
    DOI: 10.1007/s10700-020-09336-7
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    References listed on IDEAS

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    1. Qinyun Lu & Yuanguo Zhu, 2020. "Finite-time stability of uncertain fractional difference equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 239-249, June.
    2. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. 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.

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