Spectral dominance of complex roots for single-delay linear equations

This paper provides necessary and sufficient conditions for the existence of a pair of complex conjugate roots, each of multiplicity two, in the spectrum of a linear time-invariant single-delay equation of retarded type. This pair of roots is also shown to be always strictly dominant, determining thus the asymptotic behavior of the system. The proof of this result is based on the corresponding result for real roots of multiplicity four, continuous dependence of roots with respect to parameters, and the study of crossing imaginary roots. We also present how this design can be applied to vibration suppression and flexible mode compensation.

Mots clés

time-delay equations stability analysis spectral methods root assignment crossing imaginary roots

Domaines

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

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https://hal.science/hal-02422707

Soumis le : vendredi 8 mai 2020-23:43:15

Dernière modification le : lundi 18 mars 2024-03:05:37

Dates et versions

hal-02422707 , version 1 (23-12-2019)

hal-02422707 , version 2 (08-05-2020)

Identifiants

HAL Id : hal-02422707 , version 2
ARXIV : 2002.07267
DOI : 10.1016/j.ifacol.2020.12.062

Citer

Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu, Tomas Vyhlidal. Spectral dominance of complex roots for single-delay linear equations. IFAC 2020 - 21st IFAC World Congress, IFAC, Jul 2020, Berlin / Virtual, Germany. ⟨10.1016/j.ifacol.2020.12.062⟩. ⟨hal-02422707v2⟩

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