Design of \(H_{\infty}\)-control for fuzzy time-delay systems
type: Item
instance of: scholarly article
title: Design of \(H_{\infty}\)-control for fuzzy time-delay systems
zbMATH Open document ID: 1083.93014
author: Jun Yoneyama
published in: Fuzzy Sets and Systems
publication date: 2005-04-07T00:00:00Z
review text: Design problems of \(H_{\infty}\) output feedback controllers for Takagi-Sugeno (TS) fuzzy time-delay systems are considered. TS fuzzy time-delay systems and the \(H_{\infty}\) performance (norm) for stable fuzzy time-delay systems are intoduced. Systems with multiple time-delays in the state are considered. A sufficient condition for the norm being less than a given number is provided. Further, the \(H_{\infty}\)-problem with output feedback controllers is considered. Both memoryless controllers and controllers with memory are designed. In the design of output feedback controllers, the selection of the premise variables in the IF-THEN rules is important. For the premise variables, three cases are considered: (i) the premise variable is given and can be used in the controller design, (ii) the premise variable coincides with the output of the underlying system, (iii) the premise variable coincides with the state of the system which is unobservable. In the first two cases the author proposes a design method, based on the linear theory, of \(H_{\infty}\) controllers and sufficient conditions which guarantee the required \(H_{\infty}\) performance of the closed-loop systems. In the last case, an \(H_{\infty}\) controller for an approximation of the original system is given. Two examples are given to illustrate the applicability of the proposed methodology.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 15A39
zbMATH DE Number: 2153575
zbMATH Keywords: \(H_{\infty}\)-control
zbMATH Keywords: Takagi-Sugeno fuzzy time delay systems
zbMATH Keywords: linear matrix inequalities
zbMATH Keywords: output feedback
zbMATH Keywords: premise variables
MaRDI profile type: Publication
full work available at URL: j.fss.2004.04.015
OpenAlex ID: W1984831507
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DOI: 10.1016/J.FSS.2004.04.015
description: scientific article; zbMATH DE number 2153575