On the Weierstrass preparation theorem with applications to the asymptotic analysis of characteristics roots of time-delay systems

M. F. Barrios; S. I. Niculescu; J. Chen; V. M. Cárdenas-Galindo

doi:10.1016/j.ifacol.2015.09.386

On the Weierstrass preparation theorem with applications to the asymptotic analysis of characteristics roots of time-delay systems

M. F. Barrios, S. I. Niculescu, J. Chen, V. M. Cárdenas-Galindo

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	251-256
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	48
Issue number	12
DOIs	https://doi.org/10.1016/j.ifacol.2015.09.386
Publication status	Published - 1 Jul 2015
Event	12th IFAC Workshop on Time Delay Systems, TDS 2015 - Ann Arbor, United States Duration: 28 Jun 2015 → 30 Jun 2015

Research Keywords

Crossing directions
Newton-diagram
Puiseux series
Weierstrass Polynomial

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title = "On the Weierstrass preparation theorem with applications to the asymptotic analysis of characteristics roots of time-delay systems",

abstract = "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.",

keywords = "Crossing directions, Newton-diagram, Puiseux series, Weierstrass Polynomial",

author = "Barrios, {M. F.} and Niculescu, {S. I.} and J. Chen and C{\'a}rdenas-Galindo, {V. M.}",

year = "2015",

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day = "1",

doi = "10.1016/j.ifacol.2015.09.386",

language = "English",

volume = "48",

pages = "251--256",

journal = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

issn = "1474-6670",

publisher = "IFAC Secretariat",

number = "12",

note = "12th IFAC Workshop on Time Delay Systems, TDS 2015 ; Conference date: 28-06-2015 Through 30-06-2015",

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On the Weierstrass preparation theorem with applications to the asymptotic analysis of characteristics roots of time-delay systems. / Barrios, M. F.; Niculescu, S. I.; Chen, J. et al.
In: IFAC Proceedings Volumes (IFAC-PapersOnline), Vol. 48, No. 12, 01.07.2015, p. 251-256.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - On the Weierstrass preparation theorem with applications to the asymptotic analysis of characteristics roots of time-delay systems

AU - Barrios, M. F.

AU - Niculescu, S. I.

AU - Chen, J.

AU - Cárdenas-Galindo, V. M.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - 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.

AB - 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.

KW - Crossing directions

KW - Newton-diagram

KW - Puiseux series

KW - Weierstrass Polynomial

U2 - 10.1016/j.ifacol.2015.09.386

DO - 10.1016/j.ifacol.2015.09.386

M3 - RGC 21 - Publication in refereed journal

SN - 1474-6670

VL - 48

SP - 251

EP - 256

JO - IFAC Proceedings Volumes (IFAC-PapersOnline)

JF - IFAC Proceedings Volumes (IFAC-PapersOnline)

IS - 12

T2 - 12th IFAC Workshop on Time Delay Systems, TDS 2015

Y2 - 28 June 2015 through 30 June 2015

ER -

On the Weierstrass preparation theorem with applications to the asymptotic analysis of characteristics roots of time-delay systems

Abstract

Research Keywords

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