Observer design for discrete type-1 and type-2 TSK fuzzy systems

This paper proposes a new observer design methodology for type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems. The design methodology does not require a common Lyapunov function and is therefore applicable to systems with non-detectable consequents. Our observers include fuzzy observers as well as constant gain observers. The observers are exponentially stable and the designer can specify the rate of exponential convergence. The observer designs can be tested using linear matrix inequalities (LMIs). The design methodology is demonstrated using two examples, the Tora system and the inverted pendulum. The results show that the observer design provides good estimates of the state even if the system has non-detectable consequents.