IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v142y2009i3d10.1007_s10957-009-9527-2.html
   My bibliography  Save this article

Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods

Author

Listed:
  • M. S. Mahmoud

    (King Fahd University of Petroleum and Minerals)

  • P. Shi

    (University of Glamorgan
    Victoria University
    University of South Australia)

  • A. W. A. Saif

    (King Fahd University of Petroleum and Minerals)

Abstract

This paper presents new results pertaining to the delay-dependent stability and control synthesis of a class of linear switched continuous-time systems with time-varying delays. A new state transformation is introduced to exhibit the delay-dependent dynamics in the slow-time scale. For stability, we construct an appropriate selective Lyapunov functional to derive delay-dependent LMI-based sufficient conditions under arbitrary switching and without relying to overbounding. For the control synthesis, we design switched feedback schemes based on quadratic ℋ2, ℋ∞ and simultaneous ℋ2/ℋ∞ performance criteria. Under the developed transformation, it is established that both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.

Suggested Citation

  • M. S. Mahmoud & P. Shi & A. W. A. Saif, 2009. "Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 583-601, September.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9527-2
    DOI: 10.1007/s10957-009-9527-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-009-9527-2
    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/s10957-009-9527-2?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. 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.
    2. Peng Shi & Yanyan Yin & Fei Liu, 2013. "Gain-Scheduled Worst-Case Control on Nonlinear Stochastic Systems Subject to Actuator Saturation and Unknown Information," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 844-858, March.

    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:142:y:2009:i:3:d:10.1007_s10957-009-9527-2. 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.