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Finite-time stabilization of time-varying nonlinear systems based on a novel differential inequality approach

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  • Wu, Jie
  • He, Xinyi
  • Li, Xiaodi

Abstract

In this paper, the finite-time stabilization problem is investigated for a class of time-varying nonlinear systems. The classical finite-time differential inequality is extended to time-varying systems and some new lemmas are derived for global finite-time stability (FTS) and local FTS of the corresponding closed-loop systems. Then based on the hybrid control theory and the extended time-varying differential inequality, we present two control schemes including continuous control and hybrid control. It is shown that the continuous control is formulated to make the system converge in finite time, while the impulsive part involved in hybrid control accelerates the stabilization. In addition, the theoretical results are applied to the finite-time synchronization of complex networks with time-varying parametric matrices. Ultimately, two numerical examples are presented to demonstrate the distinctiveness and the effectiveness of our proposed results.

Suggested Citation

  • Wu, Jie & He, Xinyi & Li, Xiaodi, 2022. "Finite-time stabilization of time-varying nonlinear systems based on a novel differential inequality approach," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    • Handle: RePEc:eee:apmaco:v:420:y:2022:i:c:s0096300321009784
    DOI: 10.1016/j.amc.2021.126895
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    References listed on IDEAS

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    1. He, Xinyi & Li, Xiaodi & Nieto, Juan J., 2021. "Finite-time stability and stabilization for time-varying systems," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
    3. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
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    1. Jiang, Ziling & Huang, Fan & Shao, Haijian & Cai, Shuiming & Lu, Xiaobo & Jiang, Shengqin, 2023. "Time-varying finite-time synchronization analysis of attack-induced uncertain neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Gao, Zilin & Guo, Changyuan & Li, Yongfu & Liu, Lizhi & Luo, Weimin, 2023. "Stabilization of a structurally balanced complex network with similar nodes of different dimensions," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. Xing, Ying & He, Xinyi & Li, Xiaodi, 2023. "Lyapunov conditions for finite-time stability of disturbed nonlinear impulsive systems," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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