On the stability of continuous-time positive switched systems

Continuous-time positive systems, switching among p subsystems, are introduced, and a complete characterization for the existence of a common linear copositive Lyapunov function for all the subsystems is provided. In particular, the existence of such a Lyapunov function is related to the existence of common quadratic copositive Lyapunov functions. When the subsystems are obtained by applying different feedback control laws to the same continuous-time single-input positive system, the above characterization leads to a very easy checking procedure.