IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v189y2024ip1s0960077924011834.html
   My bibliography  Save this article

Stability of nonlinear delayed impulsive control systems via step-function method

Author

Listed:
  • Wang, Yinuo
  • Li, Chuandong
  • Wu, Hongjuan
  • Deng, Hao

Abstract

In this paper, considering that the limited speed of information transfer may generate time delay, which can sometimes influence the stability of the system, but in reality time delay is pervasive, and sometimes can have a positive impact on system’s stability, so it is essential to think about its existence. The nonlinear systems under delayed impulsive control (IC) are investigated here, and we mainly utilize the multiple-spans step-function method to analyse the stability conditions of the considered systems, which can be counted as a generalization of the Lyapunov-like stability method and is less conservative compared with the existing traditional Lyapunov-like function method. Moreover, it is the first time that this method employed for the stability of systems with IC and time delay. Two examples of equidistant impulses of nonlinear autonomous system and non-equidistant impulses of linear time-varying system by using two-spans step-function method are presented to validate the utility of the presented approach, respectively. Besides, the Zeno behavior of autonomous system without time delay is provided and treated by the presented method, which can better manifest the extensive viability of the method compared with the Lyapunov-like function method.

Suggested Citation

  • Wang, Yinuo & Li, Chuandong & Wu, Hongjuan & Deng, Hao, 2024. "Stability of nonlinear delayed impulsive control systems via step-function method," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011834
    DOI: 10.1016/j.chaos.2024.115631
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924011834
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115631?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. Huan, Mingchen & Li, Chuandong, 2022. "Stability analysis of state-dependent impulsive systems via a new two-sided looped functional," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.
    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.
    4. Fang, Qi & Wang, Mingzhu & Li, Xiaodi, 2023. "Event-triggered distributed delayed impulsive control for nonlinear systems with applications to complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    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. 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).
    2. 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).
    3. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Bei Zhang & Yonghui Xia & Lijuan Zhu & Haidong Liu & Longfei Gu, 2019. "Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    5. Hu, Jingting & Sui, Guixia & Li, Xiaodi, 2020. "Fixed-time synchronization of complex networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. 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).
    7. Liu, Zhengli & Luo, Mengzhuo & Cheng, Jun & Shi, Kaibo, 2025. "Synchronization control of partial-state-based neural networks: Event-triggered impulsive control with distributed actuation delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 657(C).
    8. Gani Stamov & Ivanka Stamova, 2019. "Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds," Mathematics, MDPI, vol. 7(11), pages 1-15, October.
    9. 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.
    10. Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2020. "p th Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays," Mathematics, MDPI, vol. 8(2), pages 1-10, February.
    11. He, Xinyi & Wang, Yuhan & Li, Xiaodi, 2021. "Uncertain impulsive control for leader-following synchronization of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    12. Gang Zhang & Yinfang Song & Xiaoyou Liu, 2024. "Exponential Synchronization of Coupled Neural Networks with Hybrid Delays and Stochastic Distributed Delayed Impulses," Mathematics, MDPI, vol. 12(13), pages 1-22, June.
    13. Miaadi, Foued & Li, Xiaodi, 2021. "Impulsive effect on fixed-time control for distributed delay uncertain static neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    14. K., Pooja Lakshmi & Senthilkumar, T., 2024. "Synchronization results for uncertain complex-valued neural networks under delay-dependent flexible impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    15. Yu, Tianhu & Cao, Dengqing & Yang, Yang & Liu, Shengqiang & Huang, Wenhu, 2016. "Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 92-101.
    16. Fan, Hongguang & Chen, Xijie & Shi, Kaibo & Wen, Hui, 2024. "Distributed delayed impulsive control for μ-synchronization of multi-link structure networks with bounded uncertainties and time-varying delays of unmeasured bounds: A novel Halanay impulsive inequali," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    17. Neshat, Mehdi & Nezhad, Meysam Majidi & Abbasnejad, Ehsan & Mirjalili, Seyedali & Groppi, Daniele & Heydari, Azim & Tjernberg, Lina Bertling & Astiaso Garcia, Davide & Alexander, Bradley & Shi, Qinfen, 2021. "Wind turbine power output prediction using a new hybrid neuro-evolutionary method," Energy, Elsevier, vol. 229(C).
    18. Zhu, Chenhong & Li, Xiaodi & Wang, Kening, 2020. "An anti-windup approach for nonlinear impulsive system subject to actuator saturation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    19. 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).
    20. 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).

    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:chsofr:v:189:y:2024:i:p1:s0960077924011834. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.