A Hamilton-Jacobi inequality approach to the strict \(H_ \infty\) control problem of nonlinear systems
type: Item
instance of: scholarly article
title: A Hamilton-Jacobi inequality approach to the strict \(H_ \infty\) control problem of nonlinear systems
zbMATH Open document ID: 0848.93020
DOI: 10.1016/0005-1098(95)00182-4
author: Jun-Ichi Imura
author: Toshiharu Sugie
author: Tsuneo Yoshikawa
published in: Automatica
publication date: 1996-10-28T00:00:00Z
review text: The authors study an \(H^\infty\) problem with nonlinear dynamics with respect to the state variable \(x\) but affine with respect to the control variable \(u\). The strict problem of \(H^\infty\) type is studied: to find a constant \(\gamma\) and a controller such that the associated \(\mathbb{L}^2\)-gain is less (strictly) than \(\gamma\). In this paper, conditions of existence of dissipative functions, of feedback control, and of output feedback are studied through suitable Hamilton-Jacobi inequalities for regular functions (at least \(C^1\)).
reviewed by: Marc Quincampoix
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 885877
zbMATH Keywords: \(H^ \infty\) problem
zbMATH Keywords: nonlinear
zbMATH Keywords: Hamilton-Jacobi inequalities
MaRDI profile type: Publication
full work available at URL: 0005-1098(95)00182-4
OpenAlex ID: W2095348162
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description: scientific article; zbMATH DE number 885877