On complex stability radii for implicit discrete time systems
type: Item
instance of: scholarly article
title: On complex stability radii for implicit discrete time systems
zbMATH Open document ID: 1096.93030
author: Nguyen Huu Du
author: Dao Thi Lien
author: Vu Hoang Linh
published in: Vietnam Journal of Mathematics
publication date: 2005-02-11T00:00:00Z
review text: For linear, discrete-time, regular, asymptotically stable descriptor systems \[ A x_{n+1}=Bx_n\tag{1} \] with constant coefficients \(A\) and \(B\), complex stability radii w.r.t. structured perturbations in \(A\) and \(B\) are investigated. To be more precise, let \(A,B,E,F\) be complex matrices, where \(A\), \(B\) and \(EF\) are square and of the same size and (1) is asymptotically stable, i.e., \(\rho(A,B)<1\), where \(\rho(A,B)\) is the spectral radius of the pencil \((A,B)\). Complex stability radii are defined by \[ r_C=\inf\{\|\Delta\|\,|\,\rho(A,B+E\Delta F)\geq 1, \Delta\text{ a complex matrix}\} \] and \[ r_L=\inf\{\|\Delta\|\,|\,\rho(A+E\Delta F,B)\geq 1, \Delta\text{ a complex matrix}\}, \] where \(\|\cdot\|\) is an arbitrary operator norm. Formulas for \(r_C\) and \(r_L\) in terms of the transfer function \(s\mapsto F(sA-B)^{-1}E\) are presented, and further aspects of \(r_C\) and \(r_L\) are discussed.
reviewed by: Gunther Reißig
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 2133577
zbMATH Keywords: complex stability radii
zbMATH Keywords: discrete-time descriptor systems
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2133577