MURAL - Maynooth University Research Archive Library



    Quadratic Lyapunov Functions for Systems with State-Dependent Switching


    Griggs, Wynita M. and King, Christopher K. and Shorten, Robert N. and Mason, Oliver and Wulff, Kai (2010) Quadratic Lyapunov Functions for Systems with State-Dependent Switching. Linear Algebra and its Applications, 333 (1). pp. 52-63. ISSN 0024-3795

    [img] Download (203kB)


    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...



    Add this article to your Mendeley library


    Abstract

    In this paper, we consider the existence of quadratic Lyapunov functions for certain types of switched linear systems. Given a partition of the state-space, a set of matrices (linear dynamics), and a matrix-valued function A(x) constructed by associating these matrices with regions of the state-space in a manner governed by the partition, we ask whether there exists a positive definite symmetric matrix P such that A(x)T P +PA(x) is negative definite for all x(t). For planar systems, necessary and sufficient conditions are given. Extensions for higher order systems are also presented.

    Item Type: Article
    Additional Information: Preprint version of original published article. The original article is available at http://dx.doi.org/10.1016/j.laa.2010.02.011
    Keywords: Hybrid Systems; Lyapunov Functions; Quadratic Stability;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 3603
    Depositing User: Dr. Robert Shorten
    Date Deposited: 25 Apr 2012 15:22
    Journal or Publication Title: Linear Algebra and its Applications
    Publisher: Elsevier
    Refereed: No
    URI:

    Repository Staff Only(login required)

    View Item Item control page

    Downloads

    Downloads per month over past year