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    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

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    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
    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
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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