Observer-based controller synthesis for model-based fuzzy systems via linear matrix inequalities

In this chapter, we extend some recent results regarding the stability of continuous-time and discrete-time Takagi-Sugeno (T-S) fuzzy systems to the case where the system’s states are not available for measurement. We introduce the notion of a fuzzy observer, and show that the separation of closed-loop observer/controller holds. In other words, we show that the observer and controller design problems can be formulated as two separate LMI feasibility problems. Finally, we present a numerical example to show the effectiveness of our approach and discuss some future research directions