On the stability of continuous-time positive switched systems

Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete charac-terization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that all convex combinations of the system matrices are Hurwitz, be-comes equivalent to the generally weaker condition that the systems matri-ces are Hurwitz. In the special case of two-dimensional systems, this allows to draw a complete characterization of asymptotic stability. Finally, the case when there are only two subsystems, possibly with commuting matrices, is investigated