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...
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doi: 10.1016/j.fss.2011.07.008
handle: 10251/60726
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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