An interpolation problem associated with \(H^{\infty}\)-optimal design in systems with distributed input lags
type: Item
instance of: scholarly article
title: An interpolation problem associated with \(H^{\infty}\)-optimal design in systems with distributed input lags
zbMATH Open document ID: 0629.93019
DOI: 10.1016/0167-6911(87)90097-1
author: Gilead Tadmor
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: A variety of \(H^{\infty}\)-optimal design problems reduce to interpolation of compressed multiplication operators, \(f(s)\to \pi_ k(w(s)f(s))\), where w(s) is a given rational function and the subspace K is of the form \(K=H^ 2\theta \phi (s)H^ 2\). Here we consider \(\phi (s)=(1-e^{\alpha -s})/(s-\alpha)\), which stands for a distributed delay in a system's input. The interpolation scheme we develop, adapts to a broader class of distributed lags, namely, those determined by transfer functions of the form \(B(e^{-s})/b(s)\), where B(z) and b(s) are polynomials and \(b(s)=0\) implies \(B(e^{-s})=0\).
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 47A70
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 93B50
zbMATH DE Number: 4025254
zbMATH Keywords: H\({}^{\infty }\)-optimal design
zbMATH Keywords: interpolation
zbMATH Keywords: distributed lags
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90097-1
OpenAlex ID: W1972796488
cites work: Weighted sensitivity minimization for delay systems
cites work: On the $H^\infty $-Optimal Sensitivity Problem for Systems with Delays
cites work: On the Nehari problem for a certain class of \(L^{\infty}\) functions appearing in control theory. II
cites work: On the Uniqueness of a Minimal Norm Representative of an Operator in the Commutant of the Compressed Shift
cites work: Q3922907
cites work: Worst case analysis in the frequency domain: The H&lt;sup&gt;∞&lt;/sup&gt;approach to control
cites work: Generalized Interpolation in H ∞
cites work: Q5332803
description: scientific article; zbMATH DE number 4025254