Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

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.

► Polynomial fuzzy models stability is studied via polynomial fuzzy Lyapunov functions. ► Nonlinear models are exactly represented via a recent fuzzy Taylor-series approach. ► Takagi–Sugeno models are a particular case of fuzzy polynomial ones thus obtained. ► Polynomial fuzzy Lyapunov functions generalize stability analysis of these models. ► Conditions thus obtained are tested via available SOS software.