On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant

Guilherme Mazanti (1, 2, 3) , Islam Boussaada (1, 2, 3) , Silviu-Iulian Niculescu (1, 2)

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

This paper presents necessary and sufficient conditions for the existence of a real root of maximal multiplicity in the spectrum of a linear time-invariant single-delay equation of retarded type. We also prove that this root is always strictly dominant, and hence determines the asymptotic behavior of the system. These results are based on improved a priori bounds on the imaginary part of roots on the complex right half-plane.

Mots clés: time-delay equations; stability analysis; spectral methods; root assignment

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

Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu. On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant. 2019. ⟨hal-02422706v1⟩