Robstness bounds of Hurwitz and Schur polynomials
type: Item
instance of: scholarly article
title: Robstness bounds of Hurwitz and Schur polynomials
zbMATH Open document ID: 0655.93062
DOI: 10.1007/BF00939814
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: The problem of robustness bounds of Hurwitz and Schur polynomials is addressed. For weighted \(L_ 2\)-norm perturbations of a Hurwitz polnomial p(s) or a Schur polynomial p(z), a new method is developed for calculating the maximal perturbation bound under which stability is preserved. We show that such a robustness bound is related to the minimum of a rational function. The new method is superior to the previous one developed by \textit{C. B. Soh}, \textit{C. S. Berger} and \textit{K. P. Dabke} [IEEE Trans. Autom. Control AC-30, 1033-1036 (1985; Zbl 0565.93054)]. Our approach also provides solutions for the perturbation polynomial \(\delta\) p(s) or \(\delta\) p(z) with minimal coefficient norm which cause \(p(s)+\delta p(s)\) or \(p(z)+\delta p(z)\) to be unstable.
Mathematics Subject Classification ID: 93D99
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 4070772
zbMATH Keywords: robustness bounds
zbMATH Keywords: Hurwitz and Schur polynomials
author: Minyue Fu
MaRDI profile type: Publication
cites work: On the stability properties of polynomials with perturbed coefficients
cites work: Invariance of the strict Hurwitz property for polynomials with perturbed coefficients
cites work: Q5566063
full work available at URL: https://doi.org/10.1007/bf00939814
OpenAlex ID: W2011465545
description: scientific article; zbMATH DE number 4070772