New results on stability and L1-gain characterization for switched positive systems: A persistent dwell time approach

Abstract

This paper is concerned with the problem of stability and L1-gain characterization for a class of switched positive systems consisting of both stable and unstable subsystems. Such systems can be modeled ingeniously as switched positive systems satisfying persistent dwell time switching. Compared to the widely used dwell time and average dwell time switching in the previous literature, persistent dwell time switching is more general due to its covering such two switchings as special cases. A new sufficient criterion ensuring the stability of switched positive systems is derived by using a persistent dwell time approach. And then an unweighted L1-gain is computed by solving a linear programming problem. The presented method in this paper may decrease the conservatism. Finally, the effectiveness and advantage of the provided method are illustrated with an example.