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

By Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu. Journal of Differential Equations, 2020

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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.

Subfields: Applied Mathematics, Control and Systems Engineering, Public Health, Environmental and Occupational Health

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