IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v421y2022ics0096300322000297.html
   My bibliography  Save this article

Finite time stability for nonsingular impulsive first order delay differential systems

Author

Listed:
  • Zada, Akbar
  • Pervaiz, Bakhtawar
  • Subramanian, Muthaiah
  • Popa, Ioan-Lucian

Abstract

This primer article focuses on the representation of solutions and finite-time stability of impulsive first-order delay differential systems. We define delayed matrix function with impulses and use variation of parameters to obtain a representation of solutions of linear systems with impulse effects. The famous classical Grownwall inequalities and properties of delayed matrix exponential with impulses are used to develop sufficient conditions for finite-time stability. In the end, we provide some examples to support the results.

Suggested Citation

  • Zada, Akbar & Pervaiz, Bakhtawar & Subramanian, Muthaiah & Popa, Ioan-Lucian, 2022. "Finite time stability for nonsingular impulsive first order delay differential systems," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000297
    DOI: 10.1016/j.amc.2022.126943
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322000297
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.126943?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. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed Salem & Rawia Babusail, 2022. "Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type," Mathematics, MDPI, vol. 10(9), pages 1-14, May.

    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. Li, Mingyue & Chen, Huanzhen & Li, Xiaodi, 2021. "Exponential stability of nonlinear systems involving partial unmeasurable states via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Zhu, Sanmei & Feng, Jun-e, 2021. "The set stabilization problem for Markovian jump Boolean control networks: An average optimal control approach," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    5. 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.
    6. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.
    7. He, Xinyi & Wang, Yuhan & Li, Xiaodi, 2021. "Uncertain impulsive control for leader-following synchronization of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    8. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    9. Peng, Yuanyuan & Fan, Jinjun & Gao, Min & Li, Jianping, 2021. "Discontinuous dynamics of an asymmetric 2-DOF friction oscillator with elastic and rigid impacts," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Yuxiao Zhao & Linshan Wang & Yangfan Wang, 2021. "The Periodic Solutions to a Stochastic Two-Prey One-Predator Population Model with Impulsive Perturbations in a Polluted Environment," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 859-872, September.
    11. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Controllability of Impulsive ψ -Caputo Fractional Evolution Equations with Nonlocal Conditions," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    12. Ruofeng Rao, 2019. "Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate," Mathematics, MDPI, vol. 7(7), pages 1-15, June.
    13. 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.
    14. Li, Dingshi & Lin, Yusen, 2021. "Periodic measures of impulsive stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    15. 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.
    16. 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).
    17. Ning, Di & Chen, Juan & Jiang, Meiying, 2022. "Pinning impulsive synchronization of two-layer heterogeneous delayed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    18. Cao, Jing & Fan, Jinjun, 2021. "Discontinuous dynamical behaviors in a 2-DOF friction collision system with asymmetric damping," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    19. Guo, Mengyu & Wang, Peiguang, 2024. "Finite-time stability of non-instantaneous impulsive systems with double state-dependent delays," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    20. Xiaodi Li & A. Vinodkumar & T. Senthilkumar, 2019. "Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay," Mathematics, MDPI, vol. 7(9), pages 1-22, September.

    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:421:y:2022:i:c:s0096300322000297. 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.