Stability of discrete-time positive switched linear systems with stable and marginally stable subsystems

Abstract

In this paper we investigate the stability of discrete-time positive switched linear systems. The highlight of this work is that each subsystem is only assumed to be stable or marginally stable. Some sufficient conditions, imposed on the subsystem matrices and switching signals, are established to guarantee exponential stability of the considered positive switched linear systems. An extension to the case of time-varying and unbounded delay is also given. Compared with the continuous-time counterparts in the literature, our discrete-time case is much more complicated, involving the transitive connectivity between the subsystems specified by the switching signals.