Stability analysis and L1-gain characterization for switched positive systems under dwell-time constraint

This paper deals with the problems of stability analysis and L1-gain characterization for continuous-time switched systems consisting of positive subsystems. With the aid of a discretized copositive Lyapunov function, a sufficient condition ensuring the asymptotic stability of continuous-time switched positive systems under dwell-time constraint is obtained, which can be checked via linear programming. Furthermore, the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive Lyapunov function is obtained. The result is then extended to L1-gain characterization for switched positive systems. With a prescribed dwell time, an unweighted L1-gain can be computed via solving a linear programming problem. A numerical example and a practical traffic example are given to illustrate our results.