Fuzzy control design for nonlinear impulsive switched systems using a nonlinear Takagi-Sugeno fuzzy model

Abstract

This paper deals with the fuzzy control design for nonlinear impulsive switched systems modeled by a novel nonlinear Takagi-Sugeno (T-S) fuzzy structure. To model, this structure only uses some of the nonlinearities as premise variables. So, the derived model has fewer rules compared with the traditional T-S fuzzy models that utilize standard local sector nonlinearity; and accordingly, the number of stability/stabilization conditions is sharply reduced. In our structure, considering only a part of nonlinearities as premise variables causes that some of the local models in the consequent part of the fuzzy rules be nonlinear but with less complexity than the original nonlinear system. As a result, the feasibility of our model’s stability criteria is more than those that one can directly establish for the original nonlinear system. Besides, unlike the existing methods in the literature of impulsive switched systems that aim to permanently reduce the value of Lyapunov function candidates, this paper takes into account this process until trajectories reach a sufficient small region containing the origin. Then, within this region, the size of Lyapunov functions is just controlled at impulse instants. This strategy is useful when there are non-vanishing impulses and/or uncertainties, and it is more relaxed when the goal is ultimate bound stability. Finally, to achieve the stabilizing control signal that ensures practical control issues along with smallest ultimate bound and widest region of attraction, this paper also proposes an optimization problem with linear and bilinear constraints. The simulation results represent the performance of the proposed method.