Stability of switched linear systems on cones: A generating function approach

Abstract

This paper extends the recent study of the generating function approach to stability analysis of switched linear systems from the Euclidean space to a closed convex cone. Examples of the latter class of switched systems include switched positive systems that model various biologic and economic systems with positive states. Strong and weak stability notions are considered in this paper. In particular, it is shown that asymptotic and exponential stability are equivalent for both notions. Strong and weak generating functions on cones are introduced and their properties are established. Necessary and sufficient conditions for strong/weak exponential stability of switched linear systems on cones are obtained in terms of the radii of convergence of strong/weak generating functions.