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

Sébastien Fueyo (1) , Guilherme Mazanti (1) , Islam Boussaada (1, 2) , Yacine Chitour (3) , Silviu-Iulian Niculescu (1, 2)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 IPSA - Institut Polytechnique des Sciences Avancées
3 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: delay-differential equations; multiplicity-induced-dominancy; spectral analysis

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

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⟩