\(L_{\infty}\) approximation and nuclearity of delay systems
type: Item
instance of: scholarly article
title: \(L_{\infty}\) approximation and nuclearity of delay systems
zbMATH Open document ID: 0641.93018
DOI: 10.1016/0167-6911(88)90041-2
author: Ruth Curtain
author: Jonathan R. Partington
author: Keith Glover
author: Hans Zwart
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: Single-input single-output delay systems with transfer functions \(G(s,e^{-h_ 1s},...,e^{-h_ ks})\), where G is real rational, are considered. If h(t), \(t\geq 0\), is the impulse reponse corresponding to G, the associated Hankel operator is defined as \((\Gamma u)(t)=\int^{\infty}_{0}h(t+s)u(s)ds\). \(\Gamma\) is nuclear if its sequence of singular values is summable. Theorem 2.1 gives explicit necessary and sufficient conditions for the simultaneous nuclearity of \(\Gamma\) and the finiteness of the number of unstable poles of G. Theorem 3.1 establishes the uniform convergence in the right halfplane of the spectral approximations to G (with rate of convergence estimated). Two numerical examples are presented.
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93B15
zbMATH DE Number: 4045570
zbMATH Keywords: Single-input single-output delay systems
zbMATH Keywords: Hankel operator
zbMATH Keywords: nuclearity
zbMATH Keywords: spectral approximations
Wikidata QID: Q56319575
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90041-2
OpenAlex ID: W2021881468
cites work: Q5728644
cites work: Q3925395
cites work: Controller design for distributed systems based on Hankel-norm approximations
cites work: Partial fraction expansions for delay systems
cites work: Rational approximation of a class of infinite-dimensional systems. I: Singular values of Hankel operators
description: scientific article; zbMATH DE number 4045570