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arXiv · 2002.06128

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

Guilherme Mazanti·Islam Boussaada·Silviu-Iulian Niculescu
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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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Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu. 2020-07-11. Multiplicity-induced-dominancy for delay-differential equations of retarded type. https://doi.org/10.1016/j.jde.2021.03.003

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