IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v35y2008i3p442-451.html
   My bibliography  Save this article

Nonlinear H∞ control of stochastic time-delay systems with Markovian switching

Author

Listed:
  • Wei, Guoliang
  • Wang, Zidong
  • Shu, Huisheng

Abstract

In this paper, the stabilization and H∞ control problems are investigated for a class of stochastic time-delay systems with both nonlinear disturbances and Markovian jumping parameters. The purpose of the stochastic stabilization problem is to design a memoryless state feedback controller such that, for the addressed nonlinear disturbances as well as Markovian jumping parameters, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. In the H∞ control problem, in addition to the mean-square exponential stability requirement, a prescribed H∞ performance index is required to be achieved. By using Itô’s differential formula and the Lyapunov stability theory, sufficient conditions for the solvability of these problems are derived in term of linear matrix inequalities, which can be easily checked by resorting to available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed results.

Suggested Citation

  • Wei, Guoliang & Wang, Zidong & Shu, Huisheng, 2008. "Nonlinear H∞ control of stochastic time-delay systems with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 442-451.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:3:p:442-451
    DOI: 10.1016/j.chaos.2006.05.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906004668
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.05.015?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. Shu, Huisheng & Wei, Guoliang, 2005. "H∞ analysis of nonlinear stochastic time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 637-647.
    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. Ye, Zhiyong & Zhang, He & Zhang, Hongyu & Zhang, Hua & Lu, Guichen, 2015. "Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 156-165.

    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. Gao, Huijun & Lam, James & Wang, Zidong, 2007. "Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 394-404.
    2. Guoliang Wei & Zidong Wang & Wangyan Li & Lifeng Ma, 2014. "A Survey on Gain-Scheduled Control and Filtering for Parameter-Varying Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-10, April.
    3. Wei, Guoliang & Shu, Huisheng, 2007. "H∞ filtering on nonlinear stochastic systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 663-670.
    4. Yue, Dong & Lam, James & Wang, Zidong, 2009. "Persistent disturbance rejection via state feedback for networked control systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 382-391.

    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:35:y:2008:i:3:p:442-451. 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.