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 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

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