Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions
Bernal Reza, Miguel Ángel
- Publisher: Elsevier
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