Fuzzy-model-based exponentially stabilizing perturbed nonlinear systems in the presence of modeling error

This paper presents a systematic design procedure of fuzzy controllers for exponentially stabilizing affine nonlinear systems, which are subject to vanishing perturbations. The modeling error, as a key factor in the validity of the stability analysis is also taken into consideration. A unified framework is presented, dealing with the modeling error as the system perturbation. It is shown that the constraints imposed on the modeling error are always satisfied for affine nonlinear systems, when they are modeled by Takagi-Sugeno fuzzy model through currently available methods. The constraints required to guarantee the exponential stability of the original nonlinear system and design the controller are transformed into LMIs. Finally, the way to utilize the presented method for a stabilizing problem is demonstrated using two examples.