On the Weierstrass Preparation Theorem with Applications to the Asymptotic Analysis of Characteristics Roots of Time-Delay Systems.

This paper proposes an algorithmic approach to construct the Weierstrass Polynomial associated to the multiple characteristic roots of a time-delay system. Such a Weierstrass polynomial is employed as a tool to analize the stability behaviour of the characteristic roots with respect to small variations on the delay parameter. The proposed results are illustrated by considering several numerical examples encountered in the control literature.