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.

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

De Iuliis V.
;
Manes C.
2023-01-01

Abstract

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.
2023
979-8-3503-1140-2
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/221782
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