Stability analysis of discrete‐time switched positive linear systems with unstable subsystem

Abstract

This paper deals with the problem of stability analysis for discrete‐time switched positive linear systems with unstable subsystems. The fundamental concept involves utilizing the stability properties of switching behavior to counteract the state divergence introduced by unstable systems. Moreover, the existing results in the literature lack a method that can simultaneously address the stability analysis of switching positive systems containing only stable subsystems or containing unstable subsystems or only unstable subsystems. Therefore, in this paper, based on the widely used discretization Lyapunov function method in time‐delay systems, a new dwell‐time dependent co‐positive Lyapunov function was proposed by applying it to switched positive systems. A computable sufficient condition for stability analysis of switched linear systems with unstable subsystems was established within the dwell time framework. To verify the effectiveness of the results, this paper provides a numerical example and an example of supersaturated cross signal control for illustration, as well.