Necessary conditions for robust stability of a class of nonlinear systems
type: Item
instance of: scholarly article
title: Necessary conditions for robust stability of a class of nonlinear systems
zbMATH Open document ID: 0939.93030
DOI: 10.1016/S0005-1098(97)00231-8
author: Jorge Goncalves
author: Munther A. Dahleh
published in: Automatica
publication date: 2000-07-05T00:00:00Z
review text: Input-output stability results for feedback systems are developed. Robust stability conditions are presented for nonlinear systems with a nonlinear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small gain theorem for a class of these systems is known. Here necessary conditions are presented for the vector space (\(\ell_\infty\), \(\|\cdot\|_\infty\)). These results capture the conservatism of the small gain theory as it is applied to systems that do not have linear gain. The theory is also developed for the case of \(\ell_2\) signal norms, indicating some difficulties which make this case less natural than \(\ell_\infty\).
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93D25
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1325673
zbMATH Keywords: input-output stability
zbMATH Keywords: robust stability
zbMATH Keywords: nonlinear systems
zbMATH Keywords: small gain theorem
zbMATH Keywords: necessary conditions
zbMATH Keywords: conservatism
MaRDI profile type: Publication
full work available at URL: s0005-1098(97)00231-8
OpenAlex ID: W1975536746
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description: scientific article; zbMATH DE number 1325673