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