Stability analysis and systematic design of fuzzy controllers with simplified linear control rules

In this paper, stability analysis and systematic design procedures of fuzzy logic control systems based on the simplified Takagi-Sugeno (TS) fuzzy model are proposed. First, we represent the simplified TS model in the form of local state-space equations. Second, we show that the general TS fuzzy systems with simplified nonlinear rules are universal approximators. A systematic design procedure for fuzzy controllers is proposed through the parallel distributed compensation (PDC) scheme. Finally, necessary and sufficient conditions that guarantee stability of the fuzzy system are obtained.