On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant - Archive ouverte HAL Access content directly
Conference Papers Year : 2020

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

Abstract

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.
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Dates and versions

hal-02422706 , version 1 (23-12-2019)
hal-02422706 , version 2 (08-05-2020)

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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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