Stability radii of delay difference systems under affine parameter perturbations in infinite dimensional spaces
type: Item
instance of: scholarly article
title: Stability radii of delay difference systems under affine parameter perturbations in infinite dimensional spaces
zbMATH Open document ID: 1154.39003
author: Nguyen Khoa Son
author: Duong Dang Xuan Thanh
author: Bui The Anh
published in: Applied Mathematics and Computation
publication date: 2008-09-05T00:00:00Z
review text: The authors investigate the stability radii for delay difference systems in infinite-dimensional spaces described by a linear difference equation of the form: \[ x(t+ K+ 1)= A_0 x(t+ K)+ A_1 x(t+ K-1) +\cdots+ A_k x(t),\quad t,K\in\mathbb{N}, \] where \(A_i\in{\mathcal L}(X)\), \(i\in \overline K= \{0,1,\dots, K\}\) under arbitrary parameters of the form \[ A_i\mapsto A_i+ \sum^N_{j=1} D_{ij}\Delta_{ij} E_{ij},\quad i\in\overline K \] and \[ A_i\mapsto A_i+ \sum^N_{j=1} \delta_{ij} A_{ij},\quad i\in\overline K, \] where \(D_{ij}\in{\mathcal L}(U_{ij}, X)\), \(E_{ij}\in{\mathcal L}(X, Y_{ij})\) and \(A_{ij}\in{\mathcal L}(X)\), \(i\in\overline K\), \(j\in\overline N= \{1,2,\dots, N\}\) are given operators defining the scaling and structure of the parameter uncertainties, and \(A_{ij}\in{\mathcal L}(Y_{ij}, U_{ij})\) and \(\delta_{ij}\) are, respectively, unknown operators and scalar representing parameter uncertainties.
reviewed by: Stefan Balint
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 5321647
zbMATH Keywords: positive difference system
zbMATH Keywords: affine parameter perturbation
zbMATH Keywords: stability radius
zbMATH Keywords: delay difference systems
MaRDI profile type: Publication
full work available at URL: j.amc.2008.02.041
OpenAlex ID: W2061306585
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DOI: 10.1016/J.AMC.2008.02.041
description: scientific article; zbMATH DE number 5321647