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Journal Articles Journal of Differential Equations Year : 2021

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

Abstract

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 low-order delay-differential equations of retarded type, 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 of arbitrary order including a single delay in the system's representation. More precisely, an interesting link between characteristic functions with a real root of maximal multiplicity and Kummer's confluent hypergeometric functions is exploited. We also provide examples illustrating our main result.
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Dates and 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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Cite

Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu. Multiplicity-induced-dominancy for delay-differential equations of retarded type. Journal of Differential Equations, 2021, 286 (15), pp.84-118. ⟨10.1016/j.jde.2021.03.003⟩. ⟨hal-02479909v3⟩
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