Stability analysis of coupled differential-difference systems with multiple time-varying delays: a positivity-based approach

This work 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.