Smooth Compositions Made Stabilization of Fuzzy Systems: Easy and More Robust

Smooth fuzzy systems are the new structures of the fuzzy system which have recently taken attention for their capacity in system modeling. Hence, this article studies the stability of smooth fuzzy control systems and develops the sufficient conditions of the parameters for the stable closed-loop performance of the system. A major advantage of the presented conditions is that they do not call for a common Lyapunov function and therefore, no LMI is required to be solved to guarantee the stability of the fuzzy model. Besides, although they are the type-1 fuzzy model in nature, however, they show the high level of robustness to the noises and parametric uncertainties, which is comparable to the type-2 fuzzy models. Several comparative simulations demonstrate the capacity of the fuzzy models with the smooth compositions rather than the classical fuzzy models with the min–max or product–sum compositions.