IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v479y2024ics0096300324003370.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324003370
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128876?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. 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).
    4. 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).
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Xuemei & Liu, Xinge & Wang, Fengxian, 2023. "Anti-synchronization of fractional-order complex-valued neural networks with a leakage delay and time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Xia, Mingli & Liu, Linna & Fang, Jianyin & Qu, Boyang, 2024. "Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Lin Cao & Rongwei Guo, 2022. "Partial Anti-Synchronization Problem of the 4D Financial Hyper-Chaotic System with Periodically External Disturbance," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    5. Zhao, Shiyi & Pan, Yingnan & Du, Peihao & Liang, Hongjing, 2020. "Adaptive control for non-affine nonlinear systems with input saturation and output dead zone," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    6. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    7. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    8. Baluni, Sapna & Sehgal, Ishani & Yadav, Vijay K. & Das, Subir, 2024. "Exponential synchronization of a class of quaternion-valued neural network with time-varying delays: A Matrix Measure Approach," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Hu, Jingting & Sui, Guixia & Li, Xiaodi, 2020. "Fixed-time synchronization of complex networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    11. Wenjun Dong & Yujiao Huang & Tingan Chen & Xinggang Fan & Haixia Long, 2022. "Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    12. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Pinning impulsive cluster synchronization of uncertain complex dynamical networks with multiple time-varying delays and impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    13. He, Jin-Man & Pei, Li-Jun, 2023. "Function matrix projection synchronization for the multi-time delayed fractional order memristor-based neural networks with parameter uncertainty," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    14. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    15. Li, Zhao-Yan & Shang, Shengnan & Lam, James, 2019. "On stability of neutral-type linear stochastic time-delay systems with three different delays," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 147-166.
    16. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    17. Cui, Qian & Li, Lulu & Lu, Jianquan & Alofi, Abdulaziz, 2022. "Finite-time synchronization of complex dynamical networks under delayed impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    18. He, Xinyi & Wang, Yuhan & Li, Xiaodi, 2021. "Uncertain impulsive control for leader-following synchronization of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    19. Abdurahman, Abdujelil & Abudusaimaiti, Mairemunisa & Jiang, Haijun, 2023. "Fixed/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    20. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003370. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.