Study of the stability of fuzzy controllers by an estimation of the acctraction regions: a vector norm approach
type: Item
instance of: scholarly article
title: Study of the stability of fuzzy controllers by an estimation of the acctraction regions: a vector norm approach
zbMATH Open document ID: 1050.93056
DOI: 10.1080/10241230215288
author: J.-Y. Dieulot
author: A. El Kamel
author: Pierre Borne
published in: Mathematical Problems in Engineering
publication date: 2004-08-23T00:00:00Z
review text: The study focuses on the stability of fuzzy controllers realized in the framework of vector norms. The many-input-single-output fuzzy controller under consideration satisfies the following assumptions: (a) input fuzzy sets are described by trapezoidal membership functions, (b) AND aggregation of the conditions is realized via a minimum function, and (c) the output of the controller is formed through a singleton fuzzification. The nonlinear system under control is governed by the expression \(dx/dt = A(t, x,\omega)x + B(t,x,\omega)\) with \(\omega\) representing perturbations of the state. Following the technique of stable overvalueing systems, the stability properties of fuzzy controllers are investigated. Their attractors are formed with the aid of the comparison principle. The robustness aspects of the controllers are presented as well. A series of illustrative examples is included.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C42
zbMATH DE Number: 2094351
zbMATH Keywords: fuzzy controller
zbMATH Keywords: vector norm
zbMATH Keywords: stability
zbMATH Keywords: comparison principle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1080/10241230215288
OpenAlex ID: W2043276984
description: scientific article; zbMATH DE number 2094351