MID Property for Delay Systems: Insights on Spectral Values with Intermediate Multiplicity

TL;DR

This paper investigates the spectral properties of delay systems with intermediate multiplicity induced dominancy (MID), utilizing the Green--Hille transformation to analyze zeros of Kummer functions, advancing understanding of nonasymptotic root distributions.

Contribution

It introduces a novel approach using the Green--Hille transformation to characterize nonasymptotic zeros of Kummer functions for intermediate MID in delay systems.

Findings

Effective methodology for zero distribution analysis

Enhanced understanding of spectral values with intermediate multiplicity

Illustrative example demonstrating practical application

Abstract

This paper focuses on the problem of multiplicity induced dominancy (MID) for a class of linear time-invariant systems represented by delay-differential equations. If the problem of generic MID was characterized in terms of properties of the roots of Kummer hypergeometric functions, the case of intermediate MID is still an open problem. The aim of this paper is to address such a problem by using the Green--Hille transformation for characterizing the distribution of the nonasymptotic zeros of linear combinations of Kummer functions. An illustrative example completes the presentation and shows the effectiveness of the proposed methodology.