publication . Article . 2011

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

Thierry Marie Guerra; Antonio Sala; Abdelhafidh Jaadari; Miguel Bernal;
Open Access
  • Published: 15 Dec 2011 Journal: Fuzzy Sets and Systems, volume 185, pages 5-14 (issn: 0165-0114, Copyright policy)
  • Publisher: Elsevier BV
  • Country: Spain
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 soft...
Subjects
free text keywords: Logic, Artificial Intelligence, Fuzzy Lyapunov functions, Fuzzy modeling, Local stability, Polynomial fuzzy models, Sum of squares, Compact sets, Continuous time, Fuzzy models, Fuzzy structures, Local analysis, Non-linear model, Polynomial Lyapunov function, Stability analysis, State space, Takagi-Sugeno models, Lyapunov functions, Modal analysis, Polynomials, Software testing, Mathematical models, INGENIERIA DE SISTEMAS Y AUTOMATICA, Fuzzy number, Stable polynomial, Mathematical optimization, Applied mathematics, Defuzzification, Matrix polynomial, Fuzzy classification, Fuzzy set operations, Polynomial, Fuzzy subalgebra, Mathematics
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