IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v143y2009i2d10.1007_s10957-009-9560-1.html
   My bibliography  Save this article

Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays

Author

Listed:
  • M. S. Mahmoud

    (King Fahd University of Petroleum and Minerals)

  • Y. Xia

    (Beijing Institute of Technology)

Abstract

In this paper, we investigate the problems of robust delay-dependent ℒ2 gain analysis and feedback control synthesis for a class of nominally-linear switched discrete-time systems with time-varying delays, bounded nonlinearities and real convex bounded parametric uncertainties in all system matrices under arbitrary switching sequences. We develop new criteria for such class of switched systems based on the constructive use of an appropriate switched Lyapunov-Krasovskii functional coupled with Finsler’s Lemma and a free-weighting parameter matrix. We establish an LMI characterization of delay-dependent conditions under which the nonlinear switched delay system is robustly asymptotically stable with an ℒ2-gain smaller than a prescribed constant level. Switched feedback schemes, based on state measurements, output measurements or by using dynamic output feedback, are designed to guarantee that the corresponding switched closed-loop system enjoys the delay-dependent asymptotic stability with an ℒ2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.

Suggested Citation

  • M. S. Mahmoud & Y. Xia, 2009. "Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 329-355, November.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:2:d:10.1007_s10957-009-9560-1
    DOI: 10.1007/s10957-009-9560-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-009-9560-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-009-9560-1?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.

    Citations

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


    Cited by:

    1. Dan Zhang & Li Yu, 2012. "Fault-Tolerant Control for Discrete-Time Switched Linear Systems with Time-Varying Delay and Actuator Saturation," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 157-176, April.
    2. K. Ramakrishnan & G. Ray, 2011. "Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 366-384, May.
    3. Mahmoud, Magdi S. & Almutairi, Naif B., 2016. "Feedback fuzzy control for quantized networked systems with random delays," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 80-97.
    4. Chun Yin & Shouming Zhong & Xiaoyun Liu & Zijian Liu, 2011. "Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 81-99, October.

    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:spr:joptap:v:143:y:2009:i:2:d:10.1007_s10957-009-9560-1. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.