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

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]

Fichier principal

root.pdf (178.06 Ko)

Figures/bounds2.pgf (261.83 Ko)

Figures/bounds3.pgf (159.25 Ko)

Figures/sols.pgf (36.68 Ko)

Figures/zeros.pgf (34.18 Ko)

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https://hal.science/hal-02422706

Soumis le : vendredi 8 mai 2020-23:31:51

Dernière modification le : mardi 16 juillet 2024-11:56:03

Dates et versions

hal-02422706 , version 1 (23-12-2019)

hal-02422706 , version 2 (08-05-2020)

Identifiants

HAL Id : hal-02422706 , version 2
ARXIV : 2002.06146
DOI : 10.1016/j.ifacol.2020.12.2705

Citer

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. IFAC 2020 - 21st IFAC World Congress, IFAC, Jul 2020, Berlin / Virtual, Germany. ⟨10.1016/j.ifacol.2020.12.2705⟩. ⟨hal-02422706v2⟩

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