Some Remarks on the Regular Splitting of Quasi-Polynomials with Two Delays. Characterization of Double Roots in Degenerate Cases

Abstract

This paper addresses the classification of multiple critical roots of dynamical continuous linear time-invariant systems including two constant delays in their mathematical representation. By considering the associated Weierstrass polynomial and its algebraic properties, we investigate the splitting behavior of such critical roots when the delays are subject to small variations. Some degenerate cases are also considered. The effectiveness of the proposed approach is illustrated through several numerical examples.