Switched Homogeneous Copositive Lyapunov Function Approach to Switched Positive Systems

This paper addresses the stability problem of switched positive systems. The main contribution lies in three aspects. First, the method of switched homogeneous copositive Lyapunov function is proposed to reduce conservativeness of stability criterion of the system considered. Second, a necessary and sufficient condition is established for the existence of such a Lyapunov function, assuming that a switched linear positive system is given. Third, we prove that the conservativeness will reduce as the order of switched homogeneous copositive Lyapunov function increases. A numerical example is elaborated to show the advantage of the obtained results.