Fuzzy control and filter design for uncertain fuzzy systems
type: Item
instance of: scholarly article
title: Fuzzy control and filter design for uncertain fuzzy systems
zbMATH Open document ID: 1112.93003
DOI: 10.1007/978-3-540-37012-3
author: Wudhichai Assawinchaichote
author: Sing Kiong Nguang
author: Peng Shi
published in: Lecture Notes in Control and Information Sciences
publication date: 2006-11-29T00:00:00Z
review text: Most real physical systems are nonlinear in nature. Controlling and filtering nonlinear systems are still open problems due to their complexity natures. These problems become more complex when the system's parameters are uncertain. In recent years, a large number of practical control problems have involved designing a controller/filter that minimizes the worst-case ratio of output energy (filter error energy) to disturbance energy which is known as an \(H^\infty\) control (filter) problem. The \(H^\infty\) control or filter problem is able to address the issue of system parameter uncertainty, and also be applied to the typical problem of disturbance input control. The focus of this book is to establish novel methodologies for designing robust \(H^\infty\) fuzzy controllers and robust \(H^\infty\) fuzzy filters for a class of UNSs (Uncertain Nonlinear Systems), UNMJSs (Uncertain Nonlinear Markovian Jump Systems), UNSPSs (Uncertain Nonlinear Singularly Perturbed Systems) and UNSPS-MJs (Uncertain Nonlinear Singularly Perturbed Systems with Markovian Jump) which are described by a TS (Takagi-Sugeno) fuzzy system with parametric uncertainties and with/without MJs (Markovian Jump Systems). To investigate the design problems, the authors first describe a class of UNSs, UNMJSs, UNSPSs and UNSPS-MJs by a TS fuzzy system with parametric uncertainties and with/without MJs. Then, based on an LMI (Linear Matrix Inequalities) approach, the authors develop a technique for designing robust \(H^\infty\) fuzzy controllers and robust \(H^\infty\) fuzzy filters such that a given prescribed performance index is guaranteed. The book has been divided into two parts: In Part I, the new design methodology on a robust \(H^\infty\) fuzzy controller and a robust \(H^\infty\) fuzzy filter for a class of UFSs (Uncertain Fuzzy Systems) and UFMJSs (Uncertain Fuzzy Markovian Jump Systems) has been developed. This new design approach allows one to achieve designing the robust \(H^\infty\) fuzzy cont…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93C42
zbMATH DE Number: 5076748
zbMATH Keywords: fuzzy control design, \(H^\infty\) fuzzy filter design, fuzzy Markovian jump systems, fuzzy singularly perturbed systems
reviewed by: George S. Stavrakakis
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-540-37012-3
OpenAlex ID: W42929104
description: scientific article; zbMATH DE number 5076748