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Pré-Publication, Document De Travail Année : 2020

Multiplicity-induced-dominancy for delay-differential equations of retarded type

Résumé

An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability of solutions. Recent works have explored spectral techniques to show that, for some delay-differential equations of retarded type of low order, spectral values of maximal multiplicity are dominant, and hence determine the asymptotic behavior of the system, a property known as multiplicity-induced-dominancy. This work further explores such a property and shows its validity for general linear delay-differential equations of retarded type and arbitrary order with a single delay, exploiting for that purpose an interesting link between characteristic functions with a root of maximal multiplicity and Kummer's confluent hypergeometric functions.
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Dates et versions

hal-02479909 , version 1 (14-02-2020)
hal-02479909 , version 2 (12-07-2020)
hal-02479909 , version 3 (03-03-2021)

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Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu. Multiplicity-induced-dominancy for delay-differential equations of retarded type. 2020. ⟨hal-02479909v1⟩
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