Stability Analysis of Coupled Differential-Difference Systems With Multiple Time-Varying Delays:A Positivity-Based Approach

This article introduces novel results on linear coupled differential-difference systems with multiple time-varying delays. First, necessary and sufficient conditions for the positivity and delay-independent asymptotic stability of such systems are introduced. Then, exploiting the internally positive representation technique, we show how such stability results can be systematically exported to non-positive systems of the same class, yielding novel explicit sufficient conditions for their delay-independent stability. As a consequence, novel stability results on neutral-type systems, differential systems, and continuous-time difference systems with multiple delays are also obtained.

Automated summary

This article presents novel results on the stability of linear coupled differential-difference systems with multiple time-varying delays, introducing necessary and sufficient conditions for positivity and delay-independent stability, and demonstrating how these results can be systematically applied to non-positive systems. As a result, new stability results on neutral-type systems, differential systems, and continuous-time difference systems with multiple delays are obtained.