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. © 2015, IFAG.

Crossing directions; Newton-diagram; Puiseux series; Weierstrass Polynomial Algorithms; Asymptotic analysis; Delay control systems; Polynomials; Algorithmic approach; Characteristic roots; Crossing directions; Delay parameters; Multiple characteristics; Puiseux series; Small variations; Time-delay systems; Time delay

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