Generalizations of the Hermite-Biehler theorem
type: Item
instance of: scholarly article
title: Generalizations of the Hermite-Biehler theorem
zbMATH Open document ID: 0949.15037
DOI: 10.1016/S0024-3795(99)00069-5
author: Ming-Tzu Ho
author: Aniruddha Datta
author: Shankar P. Bhattacharyya
published in: Linear Algebra and its Applications
publication date: 2000-11-22T00:00:00Z
review text: The authors generalize the Hermite-Biehler theorem which characterizes the Hurwitz stability of a real polynomial \(\delta(s).\) Let \(\delta(s)\) be a real polynomial of degree \(n\) and let \(l\) and \(r\) denote the numbers of roots in the left half and the right half of the complex plane, respectively. The signature \(l-r\) of \(\delta(s)\) determines \(l\) and \(r\) since \(l+r=n.\) Let \(i\) be the square root of \(-1\) and let \(\omega\) be a real number. Then \(\delta(i\omega)=p(\omega)+iq(\omega).\) The authors find a formula expressing the signature of \(\delta(s)\) involving \(p\) and \(q\) and zeros of these functions.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 1419863
zbMATH Keywords: Hermite-Biehler theorem
zbMATH Keywords: generalized interlacing
zbMATH Keywords: stability
zbMATH Keywords: root distribution
MaRDI profile type: Publication
cites work: Q3254327
cites work: Q4180603
cites work: Robust stabilization against structured perturbations
cites work: Q4847220
cites work: Q4016483
description: scientific article; zbMATH DE number 1419863