IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v155y2019icp314-323.html
   My bibliography  Save this article

Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative

Author

Listed:
  • Li, Peng
  • Li, Xiaodi

Abstract

This paper investigates the input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained, where both types of impulses, stabilizing impulses and destabilizing impulses, are considered. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite, that allows wider applications than existing results in the literature. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.

Suggested Citation

  • Li, Peng & Li, Xiaodi, 2019. "Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 314-323.
    • Handle: RePEc:eee:matcom:v:155:y:2019:i:c:p:314-323
    DOI: 10.1016/j.matcom.2018.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418301678
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.06.010?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. Ning, Chongyang & He, Yong & Wu, Min & Zhou, Shaowu, 2015. "Indefinite derivative Lyapunov–Krasovskii functional method for input to state stability of nonlinear systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 534-542.
    2. Peng Li & Xiaodi Li & Jinde Cao, 2018. "Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative," Complexity, Hindawi, vol. 2018, pages 1-8, January.
    3. Liu, Bin & Hill, David J. & Sun, Zhijie, 2018. "Input-to-state-KL-stability and criteria for a class of hybrid dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 124-140.
    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. Wang, Yaqi & Lu, Jianquan & Cao, Jinde & Huang, Wei & Guo, Jianhua & Wei, Yun, 2020. "Input-to-state stability of the road transport system via cyber–physical optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 3-12.

    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. 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.
    2. 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).
    3. Long, Mingkang & Su, Housheng & Liu, Bo, 2019. "Second-order controllability of two-time-scale multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 299-313.
    4. Jinlong Yuan & Jun Xie & Honglei Xu & Enmin Feng & Zhilong Xiu, 2019. "Optimization for Nonlinear Uncertain Switched Stochastic Systems with Initial State Difference in Batch Culture Process," Complexity, Hindawi, vol. 2019, pages 1-15, February.
    5. Hamza Khan & József K. Tar & Imre Rudas & Levente Kovács & György Eigner, 2018. "Receding Horizon Control of Type 1 Diabetes Mellitus by Using Nonlinear Programming," Complexity, Hindawi, vol. 2018, pages 1-11, April.
    6. Li, Jinghan & Zhao, Jun, 2022. "Bumpless transfer based event-triggered control for switched linear systems with state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    7. Peng Li & Xiaodi Li & Jinde Cao, 2018. "Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative," Complexity, Hindawi, vol. 2018, pages 1-8, January.
    8. Li, Yuanen & Zhang, Huasheng & Zhang, Tingting & Geng, Han, 2023. "Interval stability/stabilization and H∞ feedback control for linear impulsive stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    9. Bin Liu & Bo Xu & Guohua Zhang & Lisheng Tong, 2019. "Review of Some Control Theory Results on Uniform Stability of Impulsive Systems," Mathematics, MDPI, vol. 7(12), pages 1-28, December.

    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:matcom:v:155:y:2019:i:c:p:314-323. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.