Design of a discontinuous observer for general non-linear TSK fuzzy systems

This paper presents a general methodology to design a discontinuous observer for a non-linear plant in the presence of external disturbances. A non-linear plant is developed through a suitable combination of a linear time invariant system (LTI) while taking advantage of a multiple TSK fuzzy model. Through extensive mathematical manipulations, an appropriate form could be reached to exercise existing capabilities in the process of observer design. Having reached the suitable form and using the basic approach of the observer design for a typical LTI, a discontinuous model-based observer with output injection is developed. The stability characteristics of the designed observer is guaranteed based on the Lyapunov's second method. Results of a simulation have been also presented for a typical 3-DOF satellite dynamics.