On properties of Hurwitz polynomials
type: Item
instance of: scholarly article
title: On properties of Hurwitz polynomials
zbMATH Open document ID: 0874.93076
author: V. S. Antonchik
published in: Automation and Remote Control
publication date: 1997-01-08T00:00:00Z
review text: A polynomial with real coefficients is called Hurwitz if all its roots have negative real parts. Fix a monic Hurwitz polynomial \(F(\lambda)= \lambda^n+ \sum_{j=1}^{n-1} a_j\lambda^j\) of degree \(n\). Using the well-known determinantal criterion for the property of being a Hurwitz polynomial, it is not difficult to see that there is \(t_1>0\) such that for every \(t>t_1\) the polynomial \(\lambda^{n+1}+ tF(\lambda)\) is Hurwitz; moreover, for any polynomial \(L(\lambda)\) of degree at most \(n\) with real coefficients, there exists \(t_2>0\) such that the polynomial \(\lambda^{n+1}+ tF(\lambda)+ L(\lambda)\) is Hurwitz for every \(t>t_2\). In the reviewed paper upper bounds for \(t_1\) and \(t_2\) are derived.
reviewed by: Leiba Rodman
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 93C80
zbMATH DE Number: 922200
zbMATH Keywords: Hurwitz polynomial
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 922200