On linear co-positive Lyapunov functions for sets of linear positive systems.

Knorn, Florian and Mason, Oliver and Shorten, Robert N. (2009) On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica, 45 (8). pp. 1943-1947. ISSN 0005-1098

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In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of "linear" stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results.

Item Type: Article
Additional Information: The original publication is available at http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V21-4WHDHWC-2-CC&_cdi=5689&_user=107385&_orig=browse&_coverDate=08%2F31%2F2009&_sk=999549991&view=c&wchp=dGLbVzW-zSkWz&md5=b9cd433ab1bce82c03c370f5955765f5&ie=/sdarticle.pdf
Keywords: Positive systems; switched systems; linear Lyapunov functions; stability theory; time-invariant; Hamilton Institute.
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1644
Identification Number: 10.1016/j.automatica.2009.04.013
Depositing User: Hamilton Editor
Date Deposited: 09 Nov 2009 11:32
Journal or Publication Title: Automatica
Publisher: Elsevier
Refereed: Yes

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