Smooth trivial vector bundle structure of the space of Hurwitz polynomials

Baltazar Aguirre-Hernández; Martín Eduardo Frías-Armenta; Fernando Verduzco

doi:10.1016/j.automatica.2009.09.011

Smooth trivial vector bundle structure of the space of Hurwitz polynomials

Baltazar Aguirre-Hernández^*, Martín Eduardo Frías-Armenta, Fernando Verduzco

^*Corresponding author for this work

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

17 Scopus citations

Abstract

Due to the importance of the robustness of stable systems, the properties of the set of Hurwitz real polynomials are interesting to study. Among these properties is that the set is an open and not a convex set, and recently it was proved that the set of Hurwitz polynomials of degree n with positive coefficients, H_n⁺, is contractible. Now, we will prove that the set H_n⁺ is a smooth trivial vector bundle over H_{n - k}⁺ of rank k.

Original language	English
Pages (from-to)	2864-2868
Number of pages	5
Journal	Automatica
Volume	45
Issue number	12
DOIs	https://doi.org/10.1016/j.automatica.2009.09.011
State	Published - Dec 2009
Externally published	Yes

Keywords

Geometry of Hurwitz polynomials
Hurwitz polynomials
Smooth vector bundle

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abstract = "Due to the importance of the robustness of stable systems, the properties of the set of Hurwitz real polynomials are interesting to study. Among these properties is that the set is an open and not a convex set, and recently it was proved that the set of Hurwitz polynomials of degree n with positive coefficients, Hn+, is contractible. Now, we will prove that the set Hn+ is a smooth trivial vector bundle over Hn - k+ of rank k.",

keywords = "Geometry of Hurwitz polynomials, Hurwitz polynomials, Smooth vector bundle",

author = "Baltazar Aguirre-Hern{\'a}ndez and Fr{\'i}as-Armenta, {Mart{\'i}n Eduardo} and Fernando Verduzco",

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AU - Aguirre-Hernández, Baltazar

AU - Frías-Armenta, Martín Eduardo

AU - Verduzco, Fernando

PY - 2009/12

Y1 - 2009/12

N2 - Due to the importance of the robustness of stable systems, the properties of the set of Hurwitz real polynomials are interesting to study. Among these properties is that the set is an open and not a convex set, and recently it was proved that the set of Hurwitz polynomials of degree n with positive coefficients, Hn+, is contractible. Now, we will prove that the set Hn+ is a smooth trivial vector bundle over Hn - k+ of rank k.

AB - Due to the importance of the robustness of stable systems, the properties of the set of Hurwitz real polynomials are interesting to study. Among these properties is that the set is an open and not a convex set, and recently it was proved that the set of Hurwitz polynomials of degree n with positive coefficients, Hn+, is contractible. Now, we will prove that the set Hn+ is a smooth trivial vector bundle over Hn - k+ of rank k.

KW - Geometry of Hurwitz polynomials

KW - Hurwitz polynomials

KW - Smooth vector bundle

UR - http://www.scopus.com/inward/record.url?scp=70449732130&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2009.09.011

DO - 10.1016/j.automatica.2009.09.011

M3 - Artículo

SN - 0005-1098

VL - 45

SP - 2864

EP - 2868

JO - Automatica

JF - Automatica

IS - 12

ER -

Smooth trivial vector bundle structure of the space of Hurwitz polynomials

Abstract

Keywords

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