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

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.

References in corpus (5)

• Multiplicity-induced-dominancy for delay-differential equations of retarded type
• Partial Pole Placement via Delay Action: A Python Software for Delayed Feedback Stabilizing Design
• Effects of Roots of Maximal Multiplicity on the Stability of Some Classes of Delay Differential-Algebraic Systems: The Lossless Propagation Case
• Some Remarks on the Location of Non-Asymptotic Zeros of Whittaker and Kummer Hypergeometric Functions
• Spectral dominance of complex roots for single-delay linear equations

Cited by in corpus (7)

• On the pole placement of scalar linear delay systems with two delays
• Stability, Delays and Multiple Characteristic Roots in Dynamical Systems: A Guided Tour
• New Features of P3$\delta$ software: Partial Pole Placement via Delay Action
• MID Property for Delay Systems: Insights on Spectral Values with Intermediate Multiplicity
• New Features of P3$\delta$ Software. Insights and Demos
• A novel necessary and sufficient condition for the stability of $2\times 2$ first-order linear hyperbolic systems
• Padé Approximation and Hypergeometric Functions: A Missing Link with the Spectrum of Delay-Differential Equations