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

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.