Estimate of the stability radius of infinite-dimensional systems
type: Item
instance of: scholarly article
title: Estimate of the stability radius of infinite-dimensional systems
zbMATH Open document ID: 0970.93033
author: N. A. Bobylev
author: A. V. Bulatov
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: For a compact operator \(A\) on a real Hilbert space \(H\) with spectrum contained in the open left-half plane, the authors study the question when the perturbed operator \(-\tau I+ A+B\) still has its spectrum in the open left half plane. First, they prove that the supremum over the real part of the spectrum of a compact operator \(Q\) equals \(\inf_{T\in{\mathcal L}(H)} \sup_{\|x\|= 1}\langle T^{-1}QTX, x\rangle\). Using this result they obtain a condition on \(B\) which guarantees that the spectrum of \(-\tau I+ A+ B\) has its spectrum in the open left half plane. The condition on \(B\) is in terms of the Hilbert-Schmidt norm, i.e., \(\sqrt{\sum_{k,l}\langle Be_k, e_l\rangle^2}\), where \(\{e_k\}\) is an orthonormal basis of \(H\).
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1557684
zbMATH Keywords: compact operator
zbMATH Keywords: perturbed operator
zbMATH Keywords: spectrum
zbMATH Keywords: Hilbert-Schmidt norm
reviewed by: Hans Zwart
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557684