Is set modeling of white noise a good tool for robust \({\mathcal H}_2\) analysis?
type: Item
instance of: scholarly article
title: Is set modeling of white noise a good tool for robust \({\mathcal H}_2\) analysis?
zbMATH Open document ID: 0941.93016
DOI: 10.1016/S0005-1098(99)00137-5
author: Jorge Tierno
author: Mario Sznaier
published in: Automatica
publication date: 2000-04-10T00:00:00Z
review text: The main purpose of the paper is to indicate weak properties of an approximate set membership modelling of white noise proposed by \textit{F. Paganini} [see, e.g., IEEE Trans. Autom. Control 41, 1453-1465 (1996; Zbl 0864.93088)]. This approach is a useful tool for \(H_2\) analysis and design of systems without uncertainty. Nevertheless its use for worst case design of uncertain systems is doubtful since it leads to conservative results by a factor of square roots of the exogenous signal dimension. The authors show that the conservatism is the feature of this technique no matter whether the spectral or the state space approach is applied. As a consequence, the authors claim that the problem of obtaining convex tight bounds on the worst case \(H_2\) performance in the presence of uncertainty is not solved.
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 1394979
zbMATH Keywords: set membership modelling
zbMATH Keywords: \(H_2\) analysis
zbMATH Keywords: design
zbMATH Keywords: conservative results
zbMATH Keywords: worst case \(H_2\) performance
reviewed by: Andrzej Świerniak
MaRDI profile type: Publication
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full work available at URL: s0005-1098(99)00137-5
OpenAlex ID: W2167859966
description: scientific article; zbMATH DE number 1394979