Control Synthesis for Discrete-Time T–S Fuzzy Systems Based on Membership Function-Dependent $H_{\infty }$ Performance

This article focuses on disturbance attenuation problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems. First, a membership function-dependent <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index is proposed, by which, different performance can be achieved for local subsystems. Then, the better performance may be obtained for the T–S fuzzy system that works on a particular local subsystem most of the time. It may guarantee better control effects in practical engineering applications. With the help of the newly defined performance index and fuzzy Lyapunov functions, an observer-based feedback control scheme is presented in the form of linear matrix inequalities. In simulation, the performance index obtained by this article can be improved by about <inline-formula><tex-math notation="LaTeX">$10\%$</tex-math></inline-formula> than that obtained by the traditional <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control method.