On the stabilizability of discrete-time positive switched systems

In this paper we consider the class of discretetime systems switching between an arbitrary number p of autonomous positive subsystems. Necessary and sufficient conditions for the existence of (either linear or quadratic) copositive Lyapunov functions, whose values can be decreased in every positive state, by suitably choosing one of p subsystems, are obtained. When these conditions are fulfilled, state-dependent switching strategies, which prove to be stabilizing, can be adopted. Finally, the performances of these Lyapunov based strategies are compared.