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, 3) , Guilherme Mazanti (1, 2) , Silviu-Iulian Niculescu (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 IPSA - Institut Polytechnique des Sciences Avancées

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.

Mots clés: time-delay equations; multiplicity-induced-dominancy; stability analysis; confluent hypergeometric functions; Kummer functions; spectral methods; root assignment

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Automatique / Robotique

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, 2022, 360, pp.349-369. ⟨10.5802/crmath.293⟩. ⟨hal-03298718v2⟩