The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions

TL;DR

This paper extends the multiplicity-induced-dominancy property to a broad class of delay-differential equations, linking delay-system characteristics to zeros of Kummer functions through integral representations.

Contribution

It generalizes previous results to include retarded and neutral delay systems using hypergeometric functions, broadening the theoretical understanding of delay-system stability.

Findings

Validity of the property for a general class of delay equations

Connection between delay characteristics and zeros of Kummer functions

Use of hypergeometric functions in stability analysis

Abstract

In this paper, which is a direct continuation and generalization of the recent works by the authors [https://doi.org/10.1051/cocv/2019073, https://doi.org/10.1016/j.jde.2021.03.003], we show the validity of the generic multiplicity-induced-dominancy property for a general class of linear functional differential equations with a single delay, including the retarded as well as the neutral cases. The result is based on an appropriate integral representation of the corresponding characteristic quasipolynomial functions involving some appropriate degenerate hypergeometric functions.