Piecewise reconstruction of membership function approximation errors for Takagi–Sugeno fuzzy control

Abstract

We propose a conservative relaxed control method to stabilize Takagi–Sugeno (TS) fuzzy systems. First, a conventional piecewise linear function approximation method is adopted to consider the membership functions’ information in the closed-loop system’s stability analysis. Subsequently, a model reconstruction method is proposed to reformulate linear approximation error terms in the TS fuzzy form, which can effectively introduce more information into stability conditions and achieve better robust control effects. Then, based on a fuzzy Lyapunov function approach, control design conditions are derived in terms of linear matrix inequalities, with less conservatism for related results in the literature. Finally, via a benchmark experiment, it is verified that the proposed method can show better robustness with fewer decision variables in robust convex conditions.