Smooth trivial vector bundle structure of the space of Hurwitz polynomials
type: Item
instance of: scholarly article
title: Smooth trivial vector bundle structure of the space of Hurwitz polynomials
zbMATH Open document ID: 1206.55018
author: Baltazar Aguirre-Hernández
author: Fernando Verduzco
author: Martín Eduardo Frías-Armenta
published in: Automatica
publication date: 2010-06-17T00:00:00Z
review text: The authors consider a Hurwitz real polynomial, that is, a real polynomial with all its roots with negative real part. It is known that the set of Hurwitz real polynomials is an open set and that it is not a convex set. Recently it was proved that the space of Hurwitz real polynomials of degree \(n\) with positive coefficients, denoted by \(\mathcal{H}^{+}_{n}\), is contractible. In this paper the authors prove that \(\mathcal{H}^{+}_{n}\) is a smooth trivial line bundle over \(\mathcal{H}^{+}_{n-1}\) and as a consequence they conclude that \(\mathcal{H}^{+}_{n}\) is a smooth trivial vector bundle over \(\mathcal{H}^{+}_{n-k}\) of rank \(k\).
reviewed by: Alice K. M. Libardi
Mathematics Subject Classification ID: 55R25
zbMATH DE Number: 5722099
zbMATH Keywords: Hurwitz polynomials
zbMATH Keywords: vector bundle
MaRDI profile type: Publication
full work available at URL: j.automatica.2009.09.011
OpenAlex ID: W2126035215
cites work: Sufficient algebraic conditions for stability of cones of polynomials
cites work: Algebraic test for the Hurwitz stability of a given segment of polynomials
cites work: Q5485394
cites work: Q4847220
cites work: A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices
cites work: Q3946815
cites work: Properties of the entire set of Hurwitz polynomials and stability analysis of polynomial families
cites work: A canonical parameter space for linear systems design
cites work: Q3254327
cites work: Mathematical Systems Theory I
cites work: Stability of polynomials with conic uncertainty
cites work: Q4196736
cites work: Inertia characteristics of self-adjoint matrix polynomials
cites work: Inverse routh table construction and stability of delay equations
DOI: 10.1016/J.AUTOMATICA.2009.09.011
description: scientific article; zbMATH DE number 5722099