Examples of extreme cases in \(\ell_ 1\) and \({\mathcal H}_ \infty\) optimization
type: Item
instance of: scholarly article
title: Examples of extreme cases in \(\ell_ 1\) and \({\mathcal H}_ \infty\) optimization
zbMATH Open document ID: 0811.49027
DOI: 10.1016/0167-6911(94)90008-6
author: Munther A. Dahleh
author: S. R. Venkatesh
published in: Systems \& Control Letters
publication date: 1995-04-10T00:00:00Z
review text: In the paper, properties of solutions in the \(\ell_ 1\) norm and \({\mathcal H}_ \infty\) norm for closed-loop transfer functions are examined. It is shown that there exist examples for which the \(\ell_ 1\) and \({\mathcal H}_ \infty\) solutions differ considerably. The examples given in the paper illustrate that minimizing of the \(\ell_ 1\) norm is not necessarily good for minimizing of the \({\mathcal H}_ \infty\) norm and conversely.
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 683631
zbMATH Keywords: robust control
zbMATH Keywords: \(\ell_ 1\)-minimization
zbMATH Keywords: \({\mathcal H}_ \infty\)- minimization
zbMATH Keywords: closed-loop transfer functions
reviewed by: Wiesław Kotarski
MaRDI profile type: Publication
full work available at URL: 0167-6911(94)90008-6
OpenAlex ID: W2169410145
cites work: Comparison of peak and RMS gains for discrete-time systems
cites work: Q4851575
cites work: Q3802944
cites work: Feedback, minimax sensitivity, and optimal robustness
description: scientific article; zbMATH DE number 683631