Multiplicity-induced-dominancy for delay-differential equations of retarded type

Abstract

An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability of solutions. Recent works have explored spectral techniques to show that, for some low-order delay-differential equations of retarded type, spectral values of maximal multiplicity are dominant, and hence determine the asymptotic behavior of the system, a property known as multiplicity-induced-dominancy. This work further explores such a property and shows its validity for general linear delay-differential equations of retarded type of arbitrary order including a single delay in the system's representation. More precisely, an interesting link between characteristic functions with a real root of maximal multiplicity and Kummer's confluent hypergeometric functions is exploited. We also provide examples illustrating our main result.

References in corpus (1)

• Partial Pole Placement via Delay Action: A Python Software for Delayed Feedback Stabilizing Design

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• MID Property for Delay Systems: Insights on Spectral Values with Intermediate Multiplicity
• Padé Approximation and Hypergeometric Functions: A Missing Link with the Spectrum of Delay-Differential Equations
• New Features of P3$\delta$ Software. Insights and Demos
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• Spectral dominance of complex roots for single-delay linear equations
• On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant