Stability of linear difference and differential inclusions
type: Item
instance of: scholarly article
title: Stability of linear difference and differential inclusions
zbMATH Open document ID: 1082.34509
DOI: 10.1023/A:1010258420380
author: Phil Diamond
author: Valery Opoitsev
published in: Automation and Remote Control
publication date: 2005-06-17T00:00:00Z
review text: If \(S\) is an \(n\)-dimensional linear space and \(A\) the matrix of a linear transformation \({\mathcal A}: S\to S,\) then the space \(S\) can always be imbedded into an \(N\)-dimensional linear space \(E,\) \(N>n,\) such that there exists an extension \({\mathcal B}: E\to E\) of \({\mathcal A}\) with a nonnegative matrix \(B\) in some base. This property and some of its applications are the subject of this paper. In particular, the authors study the extensions \(B\) of the matrix \(A\) for which the spectral radius \(\rho(B)\) is close to \(\rho(A).\) The inclusion \(x^{k+1}\in {\mathbb A} x^{k}\) is also considered, where \({\mathbb A}\) is a compact set of matrices, and it is proved that this is asymptotically stable if and only if \({\mathbb A}\) can be extended to a set \({\mathbb B}\) of nonnegative matrices \(B\) with \(\| B\| _{1}\) or \(\| B\| _{\infty}<1.\) Similar results are derived for differential inclusions.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 34D99
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 2176784
zbMATH Keywords: stability
zbMATH Keywords: differential inclusions
zbMATH Keywords: difference inclusions
MaRDI profile type: Publication
full work available at URL: a:1010258420380
OpenAlex ID: W1496718033
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description: scientific article; zbMATH DE number 2176784