IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i2p420-427.html
   My bibliography  Save this article

Integral input-to-state stability of nonlinear control systems with delays

Author

Listed:
  • Zhu, Wenli
  • Yi, Zhang

Abstract

Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.

Suggested Citation

  • Zhu, Wenli & Yi, Zhang, 2007. "Integral input-to-state stability of nonlinear control systems with delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 420-427.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:420-427
    DOI: 10.1016/j.chaos.2006.03.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906002499
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.03.032?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. Wang, Zhanfeng & Chu, Tianguang, 2006. "Delay induced Hopf bifurcation in a simplified network congestion control model," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 161-172.
    2. Park, Ju H. & Kwon, O., 2005. "Controlling uncertain neutral dynamic systems with delay in control input," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 805-812.
    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. Xiong, Lianglin & Zhong, Shouming & Ye, Mao & Wu, Shiliang, 2009. "New stability and stabilization for switched neutral control systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1800-1811.
    2. Lu, Qiu & Xiao, Min & Tao, Binbin & Huang, Chengdai & Shi, Shuo & Wang, Zhengxin & Jiang, Guoping, 2019. "Complex dynamic behaviors of a congestion control system under a novel PD1n control law: Stability, bifurcation and periodic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 242-252.
    3. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    4. Lien, Chang-Hua, 2007. "Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 889-899.
    5. Chen, Chang-Kuo & Liao, Teh-Lu & Yan, Jun-Juh, 2009. "Active queue management controller design for TCP communication networks: Variable structure control approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 277-285.
    6. Nga, J.H.C. & Iu, H.H.C. & Ling, S.H. & Lam, H.K., 2008. "Comparative study of stability in different TCP/RED models," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 977-987.
    7. Bigdeli, Nooshin & Haeri, Mohammad, 2009. "Time-series analysis of TCP/RED computer networks, an empirical study," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 784-800.
    8. Sun, Fengyun & Zhao, Yi & Zhou, Tianshou, 2007. "Identify fully uncertain parameters and design controllers based on synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1677-1682.
    9. Huang, Chuangxia & Huang, Lihong & Feng, Jianfeng & Nai, Mingyong & He, Yigang, 2007. "Hopf bifurcation analysis for a two-neuron network with four delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 795-812.
    10. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    11. Hu, H.Y. & Wang, Z.H., 2009. "Singular perturbation methods for nonlinear dynamic systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 13-27.
    12. O. M. Kwon & J. H. Park, 2008. "Exponential Stability for Time-Delay Systems with Interval Time-Varying Delays and Nonlinear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 277-293, November.

    More about this item

    Statistics

    Access and download statistics

    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:34:y:2007:i:2:p:420-427. 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.