Reconstructing models for approximation errors in Takagi–Sugeno fuzzy control under imperfect matching

This study aims to tackle the issues associated with stability analysis in Takagi–Sugeno (TS) fuzzy systems. A novel modeling technique is proposed to incorporate the approximation error information of membership functions (MFs) into the stability conditions. First, the classical piecewise linear approximation method is employed to decompose the MFs into a linear model and an associated error model. Then, a reconstruction strategy is introduced to transform the error model into a new fuzzy model, which is subsequently used to enhance the stability analysis of TS fuzzy systems. Compared with methods that consider only the extremal values of the error function, the proposed approach leads to a multiplicative enhancement in the amount of exploitable error information. Furthermore, stochastic disturbances are introduced to evaluate the robustness of the system. Finally, the effectiveness and practicality of the proposed method are validated through two simulation examples.