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Griggs, Wynita M., King, Christopher K., Shorten, Robert N., 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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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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/3603 |
| 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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