Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

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Bernal Reza, Miguel Ángel ; Sala, Antonio ; JAADARI, ABDELHAFIDH ; Guerra, Thierry-Marie (2011)
  • Publisher: Elsevier
  • Related identifiers: doi: 10.1016/j.fss.2011.07.008
  • Subject: 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

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. Bernal Reza, MÁ.; Sala, A.; Jaadari, A.; Guerra, T. (2011). Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions. Fuzzy Sets and Systems. 185(1):5-14. doi:10.1016/j.fss.2011.07.008 Senia 5 14 185 1
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