Brief paper: On linear co-positive Lyapunov functions for sets of linear positive systems

Authors:
Florian Knorn;Oliver Mason;Robert Shorten
Affiliations:
Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland;Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland;Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

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.