Asymptotic stability and decay rates of positive linear systems with unbounded delays

There are several results on the stability analysis of positive linear systems in the presence of constant or time-varying delays. However, most existing results assume that the delays are bounded. This paper studies the stability of discrete-time positive linear systems with unbounded delays. We provide a set of easily verifiable necessary and sufficient conditions for delay-independent stability of positive linear systems subject to a general class of heterogeneous time-varying delays. For two particular classes of unbounded delays, explicit expressions that bound the decay rate of the system are presented. We demonstrate that the best bound on the decay rate that our results can guarantee can be found via convex optimization. Finally, the validity of the results is demonstrated via a numerical example.