IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/723509.html
   My bibliography  Save this article

Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System

Author

Listed:
  • Omar M. Abou Al-Ola
  • Ken'ichi Fujimoto
  • Tetsuya Yoshinaga

Abstract

Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszár's I -divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I -divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas.

Suggested Citation

  • Omar M. Abou Al-Ola & Ken'ichi Fujimoto & Tetsuya Yoshinaga, 2011. "Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-12, May.
  • Handle: RePEc:hin:jnlmpe:723509
    DOI: 10.1155/2011/723509
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2011/723509.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/MPE/2011/723509.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2011/723509?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
    ---><---

    Citations

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


    Cited by:

    1. Omar M. Abou Al-Ola & Ryosuke Kasai & Yusaku Yamaguchi & Takeshi Kojima & Tetsuya Yoshinaga, 2022. "Image Reconstruction Algorithm Using Weighted Mean of Ordered-Subsets EM and MART for Computed Tomography," Mathematics, MDPI, vol. 10(22), pages 1-17, 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:hin:jnlmpe:723509. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.