An inequality for the spectral radius of an interval matrix
type: Item
instance of: scholarly article
title: An inequality for the spectral radius of an interval matrix
zbMATH Open document ID: 0915.15017
DOI: 10.1016/S0024-3795(97)00238-3
published in: Linear Algebra and its Applications
publication date: 1998-11-17T00:00:00Z
review text: The main result of this paper says that for each square interval matrix \({\mathbb A}\) a real matrix \(A\) with the property \[ \rho({\mathbb A})\leq\rho(A) \] can be constructed, where \(\rho\) on the right-hand side stands for the spectral radius whereas on the left-hand one it denotes the generalized spectral radius in the sense of \textit{I. Daubechies} and \textit{J. C. Lagarias} [Linear Algebra Appl. 161, 227-263 (1992; Zbl 0746.15015)]. Further it is proved that \[ \rho({\mathbb A})=\rho(\text{ext} {\mathbb A}), \] where \(\text{ext} {\mathbb A}\) is the set of vertices of \({\mathbb A}\). Application of these results to checking asymptotic stability of discrete time-varying linear systems is considered.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 1154654
zbMATH Keywords: interval matrix
zbMATH Keywords: spectral radius
zbMATH Keywords: asymptotic stability
zbMATH Keywords: discrete time-varying linear systems
author: Mau-Hsiang Shih
author: Yung-Yih Lur
author: Chin-Tzong Pang
reviewed by: Jiří Rohn
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1154654