On the Stability of Coupled Differential-Difference Systems with Multiple Time-Varying Delays: A Positivity-Based Approach

Vittorio De Iuliis1, Alessandro D'innocenzo2, Alfredo Germani3, Costanzo Manes3

  • 1Università degli Studi dell'Aquila
  • 2University of L'Aquila
  • 3Universita' dell'Aquila

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Regular Session

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10:00 - 12:00 | Wed 11 Dec | Méditerranée 2 | WeA02

Delay Systems I

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Abstract

This work studies linear coupled differential-difference systems, in the general case of multiple time-varying delays. The paper presents two main contributions: first, we formulate necessary and sufficient conditions for both the positivity and delay-independent asymptotic stability of this class of systems. Then, exploiting the Internally Positive Representation technique, we show how such stability results can be systematically exported to arbitrary (i.e. not necessarily positive) systems of the same class, providing a novel explicit sufficient condition for their delay-independent stability. The theoretical results are illustrated by a numerical example.

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