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

Islam Boussaada; Guilherme Mazanti; Silviu-Iulian Niculescu

doi:10.5802/crmath.293

Systèmes dynamiques, Théorie du contrôle

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

Islam Boussaada ^1,² ; Guilherme Mazanti ² ; Silviu-Iulian Niculescu ²

¹ Institut Polytechnique des Sciences Avancées (IPSA), 63 boulevard de Brandebourg, 94200 Ivry-sur-Seine, France
² Université Paris-Saclay, CNRS, CentraleSupélec, Inria, Laboratoire des signaux et systèmes, 91190, Gif-sur-Yvette, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 349-369.

Résumé

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.

Reçu le : 2021-07-23
Révisé le : 2021-10-25
Accepté le : 2021-10-26
Publié le : 2022-04-26

DOI : 10.5802/crmath.293

Classification : 34K35, 34K20, 93D15, 33C15, 33C90

Affiliations des auteurs :

Islam Boussaada ^{1, 2} ; Guilherme Mazanti ² ; Silviu-Iulian Niculescu ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Islam Boussaada and Guilherme Mazanti and Silviu-Iulian Niculescu},
     title = {The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: {When} delay-systems characteristics meet the zeros of {Kummer} functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {349--369},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.293},
     language = {en},
}

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Islam Boussaada; Guilherme Mazanti; Silviu-Iulian Niculescu. 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), pp. 349-369. doi : 10.5802/crmath.293. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.293/

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