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

Guilherme Mazanti; Islam Boussaada; Silviu-Iulian Niculescu

doi:10.1016/j.ifacol.2020.12.2705

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arXiv · 2002.06146

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

Guilherme Mazanti·Islam Boussaada·Silviu-Iulian Niculescu

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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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Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu. 2020-02-14. On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant. https://doi.org/10.1016/j.ifacol.2020.12.2705

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