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Conference Papers Year : 2021

Insights into the multiplicity-induced-dominancy for scalar delay-differential equations with two delays

Abstract

It has been observed in recent works that, for several classes of linear time-invariant time-delay systems of retarded or neutral type with a single delay, if a root of its characteristic equation attains its maximal multiplicity, then this root is the rightmost spectral value, and hence it determines the exponential behavior of the system, a property usually referred to as multiplicity-induced-dominancy (MID). In this paper, we investigate the MID property for one of the simplest cases of systems with two delays, a scalar delay-differential equation of first order with two delayed terms of order zero. We discuss the standard approach based on the argument principle for establishing the MID property for single-delay systems and some of its limitations in the case of our simple system with two delays, before proposing a technique based on crossing imaginary roots that allows to conclude that the MID property holds in our setting.
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Dates and versions

hal-03298715 , version 1 (23-07-2021)
hal-03298715 , version 2 (17-08-2021)

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Sébastien Fueyo, Guilherme Mazanti, Islam Boussaada, Yacine Chitour, Silviu-Iulian Niculescu. Insights into the multiplicity-induced-dominancy for scalar delay-differential equations with two delays. TDS 2021 - 16th IFAC Workshop on Time Delay Systems, Sep 2021, Guangzhou, China. pp.108-114, ⟨10.1016/j.ifacol.2021.11.124⟩. ⟨hal-03298715v2⟩
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