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.
Keywords
Cite
@article{arxiv.2002.06128,
title = {Multiplicity-induced-dominancy for delay-differential equations of retarded type},
author = {Guilherme Mazanti and Islam Boussaada and Silviu-Iulian Niculescu},
journal= {arXiv preprint arXiv:2002.06128},
year = {2021}
}