Observer synthesis for discrete-time T-S fuzzy system with output disturbance

This paper presents a novel observer synthesis for nonlinear discrete-time systems with output disturbance that is approximated by the Takagi-Sugeno (T-S) fuzzy model. Based on the fuzzy model and Lyapunov theory, two main theorems are derived for particular and general cases of fuzzy systems, respectively. In theorems, one key condition is proposed, under which the fuzzy observer is synthesized to estimate the system state and the output disturbance simultaneously. Furthermore, the conditions are transformed to linear matrix inequalities (LMIs) to find the parameters in the observer. Finally, the observer is illustrated effectively by a numerical example.