Stability analysis of polynomials with an approach of differential topology

Eleazar López-Flores; Baltazar Aguirre-Hernández; Martín Eduardo Frías-Armenta

doi:10.1002/asjc.3476

Stability analysis of polynomials with an approach of differential topology

Eleazar López-Flores, Baltazar Aguirre-Hernández^*, Martín Eduardo Frías-Armenta

^*Corresponding author for this work

Departamento de Matemáticas

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the Hurwitz stability of polynomials. By considering that a (Formula presented.) degree Hurwitz polynomial has its corresponding Markov parameters, we define the set (Formula presented.) in Section 3, we also define (Formula presented.). Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that (Formula presented.) is a fiber bundle with a (Formula presented.) base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices.

Original language	English
Pages (from-to)	1068-1074
Number of pages	7
Journal	Asian Journal of Control
Volume	27
Issue number	2
DOIs	https://doi.org/10.1002/asjc.3476
State	Published - Mar 2025

Bibliographical note

Publisher Copyright:
© 2024 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.

Keywords

Hankel matrix
Hurwitz polynomials
fiber bundle
stability test

Access to Document

10.1002/asjc.3476

Cite this

@article{dda62fcb37b9478493c13e1110bb6e68,

title = "Stability analysis of polynomials with an approach of differential topology",

abstract = "In this paper, we study the Hurwitz stability of polynomials. By considering that a (Formula presented.) degree Hurwitz polynomial has its corresponding Markov parameters, we define the set (Formula presented.) in Section 3, we also define (Formula presented.). Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that (Formula presented.) is a fiber bundle with a (Formula presented.) base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices.",

keywords = "Hankel matrix, Hurwitz polynomials, fiber bundle, stability test",

author = "Eleazar L{\'o}pez-Flores and Baltazar Aguirre-Hern{\'a}ndez and Fr{\'i}as-Armenta, {Mart{\'i}n Eduardo}",

note = "Publisher Copyright: {\textcopyright} 2024 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.",

year = "2025",

month = mar,

doi = "10.1002/asjc.3476",

language = "Ingl{\'e}s",

volume = "27",

pages = "1068--1074",

journal = "Asian Journal of Control",

issn = "1561-8625",

publisher = "Wiley-Blackwell",

number = "2",

}

TY - JOUR

T1 - Stability analysis of polynomials with an approach of differential topology

AU - López-Flores, Eleazar

AU - Aguirre-Hernández, Baltazar

AU - Frías-Armenta, Martín Eduardo

PY - 2025/3

Y1 - 2025/3

N2 - In this paper, we study the Hurwitz stability of polynomials. By considering that a (Formula presented.) degree Hurwitz polynomial has its corresponding Markov parameters, we define the set (Formula presented.) in Section 3, we also define (Formula presented.). Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that (Formula presented.) is a fiber bundle with a (Formula presented.) base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices.

AB - In this paper, we study the Hurwitz stability of polynomials. By considering that a (Formula presented.) degree Hurwitz polynomial has its corresponding Markov parameters, we define the set (Formula presented.) in Section 3, we also define (Formula presented.). Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that (Formula presented.) is a fiber bundle with a (Formula presented.) base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices.

KW - Hankel matrix

KW - Hurwitz polynomials

KW - fiber bundle

KW - stability test

UR - http://www.scopus.com/inward/record.url?scp=85201065433&partnerID=8YFLogxK

U2 - 10.1002/asjc.3476

DO - 10.1002/asjc.3476

M3 - Artículo

AN - SCOPUS:85201065433

SN - 1561-8625

VL - 27

SP - 1068

EP - 1074

JO - Asian Journal of Control

JF - Asian Journal of Control

IS - 2

ER -

Stability analysis of polynomials with an approach of differential topology

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Cite this