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A novel finite-time stability criteria and controller design for nonlinear impulsive systems

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  • Cheng, Mengqing
  • Zhao, Junsheng
  • Xie, Xiangpeng
  • Sun, Zong-yao

Abstract

The issue of a novel finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, two sufficient conditions for the novel finite-time stability of impulsive systems are presented, in which the stabilizing impulses and the destabilizing impulses are considered, respectively. Meanwhile, the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory with impulsive control, we design a controller for impulsive dynamical systems to satisfy the novel finite-time stability. Finally, two simulation examples are given, in which the first example demonstrates the superiority of the proposed finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller.

Suggested Citation

  • Cheng, Mengqing & Zhao, Junsheng & Xie, Xiangpeng & Sun, Zong-yao, 2024. "A novel finite-time stability criteria and controller design for nonlinear impulsive systems," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003370
    DOI: 10.1016/j.amc.2024.128876
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    References listed on IDEAS

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    1. Wei, Xiaofeng & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(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).
    4. 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.
    5. Zhao, Junsheng & Yuan, Yixuan & Sun, Zong-yao & Xie, Xiangpeng, 2023. "Applications to the dynamics of the suspension system of fast finite time stability in probability of p-norm stochastic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 457(C).
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