Some Remarks on the Stability of Time-Varying Discrete-Time Positive Delay Systems

This paper illustrates some remarkable properties of linear time-varying discrete-time positive systems with delays. First, we discuss how a well known property of positive delay systems with time-invariant matrices, namely the equivalence among delay-dependent and delay-independent stability, does not generalize to positive delay systems when the system matrices are time-varying. Then, we illustrate how a stability analysis based on the existence of linear co-positive Lyapunov functions on the zero-delay system and on its dual produces a remarkable dissimilarity to what happens in the time-invariant case: the dual condition is sufficient to prove delay-independent stability, whereas the primal is not even a stability condition. Implications and further results are discussed.