Equilibria of recurrent fuzzy systems
type: Item
instance of: scholarly article
title: Equilibria of recurrent fuzzy systems
zbMATH Open document ID: 1031.93116
DOI: 10.1016/S0165-0114(03)00069-1
author: Roland Kempf
author: Jürgen Adamy
published in: Fuzzy Sets and Systems
publication date: 2003-12-04T00:00:00Z
review text: The paper is concerned with fuzzy control systems in two directions: modelling and qualitative behavior of equilibria. The modelling part shows how recurrent fuzzy systems can be modelled by the usual control recurrence \[ x_{k+1} = f(x_k,u_k) \] and establishes some basic properties of \(f\). Further, the existence of at least one equilibrium for any constant input \(u\) is proved; since \(f\) is globally Lipschitz with the Lipschitz constant \(1\) (non-expansiveness), the authors easily prove Lyapunov stability of any equilibrium. It is also shown that chaotic motions are excluded for such systems.
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 2013117
zbMATH Keywords: recurrent fuzzy systems
zbMATH Keywords: equilibria
zbMATH Keywords: stability
zbMATH Keywords: Lipschitz systems
zbMATH Keywords: fuzzy control systems
zbMATH Keywords: Lyapunov stability
reviewed by: Vladimir Răsvan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2013117