Dynamical systems, Control theory
The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions
Comptes Rendus. Mathématique, Volume 360 (2022) no. G4, pp. 349-369.

In this paper, which is a direct continuation and generalization of the recent works by the authors [17, 35], 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.

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DOI: 10.5802/crmath.293
Classification: 34K35, 34K20, 93D15, 33C15, 33C90
Boussaada, Islam 1, 2; Mazanti, Guilherme 1; Niculescu, Silviu-Iulian 1

1 Université Paris-Saclay, CNRS, CentraleSupélec, Inria, Laboratoire des signaux et systèmes, 91190, Gif-sur-Yvette, France
2 Institut Polytechnique des Sciences Avancées (IPSA), 63 boulevard de Brandebourg, 94200 Ivry-sur-Seine, France
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Boussaada, Islam; Mazanti, Guilherme; Niculescu, Silviu-Iulian. The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions. Comptes Rendus. Mathématique, Volume 360 (2022) no. G4, pp. 349-369. doi : 10.5802/crmath.293. http://www.numdam.org/articles/10.5802/crmath.293/

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