IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v309y2017icp205-221.html
   My bibliography  Save this article

Constructive proof of Lagrange stability and sufficient – Necessary conditions of Lyapunov stability for Yang–Chen chaotic system

Author

Listed:
  • Liao, Xiaoxin
  • Zhou, Guopeng
  • Yang, Qigui
  • Fu, Yuli
  • Chen, Guanrong

Abstract

This paper studies the stability problem of Yang–Chen system. By introducing different radial unbounded Lyapunov functions in different regions, global exponential attractive set of Yang–Chen chaotic system is constructed with geometrical and algebraic methods. Then, simple algebraic sufficient and necessary conditions of global exponential stability, global asymptotic stability, and exponential instability of equilibrium are proposed. And the relevant expression of corresponding parameters for local exponential stability, local asymptotic stability, exponential instability of equilibria are obtained. Furthermore, the branch problem of the system is discussed, some branch expressions are given for the parameters of the system.

Suggested Citation

  • Liao, Xiaoxin & Zhou, Guopeng & Yang, Qigui & Fu, Yuli & Chen, Guanrong, 2017. "Constructive proof of Lagrange stability and sufficient – Necessary conditions of Lyapunov stability for Yang–Chen chaotic system," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 205-221.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:205-221
    DOI: 10.1016/j.amc.2017.03.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317302175
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.03.033?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. Ma, Qian, 2017. "Cooperative control of multi-agent systems with unknown control directions," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 240-252.
    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. Yu, Zhiyong & Jiang, Haijun & Mei, Xuehui & Hu, Cheng, 2018. "Guaranteed cost consensus for second-order multi-agent systems with heterogeneous inertias," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 739-757.
    2. Fan, Ming-Can & Wu, Yue, 2018. "Global leader-following consensus of nonlinear multi-agent systems with unknown control directions and unknown external disturbances," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 274-286.
    3. Zhang, Zhipeng & Wang, Huimin, 2022. "Resilient decentralized adaptive tracking control for nonlinear interconnected systems with unknown control directions against DoS attacks," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    4. Kaviarasan, Boomipalagan & Kwon, Oh-Min & Park, Myeong Jin & Sakthivel, Rathinasamy, 2021. "Stochastic faulty estimator-based non-fragile tracking controller for multi-agent systems with communication delay," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Xiongfeng Deng & Yiming Yuan & Lisheng Wei & Binzi Xu & Liang Tao, 2022. "Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method," Mathematics, MDPI, vol. 10(14), pages 1-13, July.

    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:309:y:2017:i:c:p:205-221. 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.