Observer based controller for nonlinear systems using Takagi-Sugeno Fuzzy model

In this paper, an observer based controller for nonlinear systems represented in Takagi Sugeno Fuzzy Logic is presented. The controller is represented in parallel distributed form and the gains are updated by network inversion. In practice, all the state variables may not be available for measurement, hence an observer is required. The observer is also represented in parallel distributed form and the gains are found by solving a set of Linear Matrix Inequalities. As the observer and the controller are both designed to be individually stable, the overall system will also be stable, and the separation property will hold. The overall system with the controller and observer is tested on two nonlinear systems — the single link manipulator and the inverted pendulum. The simulation results show that the design is viable.