Robust stability of switched positive linear systems

Abstract

The aim of the present paper is to give robust stability based on exponentially stable switched positive linear systems. Our theoretical analysis shows that if there exists a positive stable system of all positive subsystems, then a lower bound and upper bound for stability radius of the switched system under positive affine perturbations are established. In the particular case of two dimensional switched system, including two switching signals, we obtain a formula of stability radius. Several examples are provided to illustrate our approach.