Observer-Based Controller Designs Based on Separation Principle for T-S Fuzzy System with Unmeasurable Premise Variables

We propose new observer-based fuzzy controllers for general Takagi-Sugeno fuzzy system with nonlinear output equations and unmeasurable premise variables. For Takagi-Sugeno fuzzy systems with the unmeasurable premise variables, the separation principle may not hold in general. To overcome this difficulty, we employ the differential mean value theorem and the sector nonlinearity approach to reformulate as an appropriate error system in which the errors between the actual states and its estimates follow. Then, with the state feedback controller and the error system, we have an augmented closed-loop system that can independently and simultaneously analyze the stability of the states and the errors. Since our designed conditions do not require the Lipschitz condition, our approach is more relaxed than the existing approach. Finally, an illustrative example is given to show the effectiveness of the proposed approach.