A membership function-dependent L∞ performance based output interval estimation method for discrete-time Takagi–Sugeno fuzzy systems applied to fault detection

Abstract

In the design process of traditional L∞ methods, a common performance index is often considered in different fuzzy rules. This may introduce a certain conservatism when most of the whole fuzzy system operates under a certain fuzzy rule or a few fuzzy rules. Therefore, this paper focuses on robust interval estimation problems for discrete-time Takagi–Sugeno fuzzy systems, and a new membership function-dependent L∞ performance index is proposed. The proposed L∞ performance can ensure better results in practical engineering applications by using the priori knowledge that the model works most of the time on some specific fuzzy systems to design performance index. By means of fuzzy basis-dependent Lyapunov functions, a membership function-dependent L∞ performance based interval estimation strategy applied to fault detection is presented. Through simulation analysis, the L∞ index in this paper is better than the conventional one and a tighter interval estimation is obtained leading to more accurate and faster fault detection effects. Meanwhile, the simulation results of this method also reflect the membership function-dependent property well.