Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 2011 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 185, pages 5-14 (issn: 0165-0114,

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Authors: Miguel Bernal 0001; Antonio Sala 0001; Abdelhafidh Jaadari; Thierry-Marie Guerra;

doi: 10.1016/j.fss.2011.07.008

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

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Abstract

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinement of the polynomial Lyapunov function so as to make it share the fuzzy structure of the model proves advantageous. Conditions thus obtained are tested via available SOS software. © 2011 Elsevier B.V. All rights reserved.

Related Organizations

Universitat Politècnica de València
Spain
University of Valenciennes and Hainaut-Cambresis
France
Sonora Institute of Technology
Mexico

Keywords

local stability, Fuzzy modeling, Polynomial fuzzy models, Modal analysis, Takagi-Sugeno models, fuzzy Lyapunov functions, Polynomials, Software testing, Local analysis, polynomial fuzzy models, sum of squares, Fuzzy Lyapunov functions, Lyapunov functions, Asymptotic stability in control theory, Fuzzy models, Mathematical models, Compact sets, Non-linear model, Fuzzy control/observation systems, Fuzzy structures, Stability analysis, Polynomial Lyapunov function, INGENIERIA DE SISTEMAS Y AUTOMATICA, fuzzy modeling, Local stability, Continuous time, Sum of squares, State space

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