Stability analysis and systematic design of Takagi--Sugeno fuzzy control systems
type: Item
instance of: scholarly article
title: Stability analysis and systematic design of Takagi--Sugeno fuzzy control systems
zbMATH Open document ID: 1142.93373
author: Zhi Hong Xiu
author: Guang Ren
published in: Fuzzy Sets and Systems
publication date: 2005-04-07T00:00:00Z
review text: Discussed are Takagi-Sugeno models of the form \[ \begin{gathered} R_i:\text{ If }x_1(t)\text{ is }F_{1i}\text{ and }x_2(t)\text{ is }F_{2i}\text{ and}\dots x_n(t)\text{ is }F_{ni}\text{ then }dx(t)/dt= A_ix(k)+ B_i u(t),\\ i= 1,2,\dots, 1,\end{gathered} \] where \(x(t)= [x_1x_2 x_n]^T\) denotes a state vector and \((A_i, B_i)\) stands for the matrices of the corresponding local model. The extended Lyapunov stability criterion applied to the rule-based system presented above is concerned with the structural information about rules ``activated'' within some region and this helps relax the stability conditions (in which the \(n\times n\) positive definite symmetric matrix \(P\) involves only a subset of matrices \(P_1,P_2,\dots, P_r\) pertaining to the individual rules). The mechanism of stability verification is then presented. Numeric examples are also included in this study.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 2153572
zbMATH Keywords: fuzzy models
zbMATH Keywords: stability
zbMATH Keywords: fuzzy partition
zbMATH Keywords: Takagi-Sugeno model
MaRDI profile type: Publication
full work available at URL: j.fss.2004.04.008
OpenAlex ID: W2062052267
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DOI: 10.1016/J.FSS.2004.04.008
description: scientific article; zbMATH DE number 2153572