Adaptive observer design for the uncertain Takagi–Sugeno fuzzy system with output disturbance

The study proposes an adaptive fuzzy observer for the uncertain Takagi–Sugeno (T–S) fuzzy system with output disturbance. First, an augmented fuzzy model is built by integrating the system state and the output disturbance together as new variables. Then, the desired adaptive fuzzy observer is designed to estimate the unavailable system state and the unknown output disturbance simultaneously. Based on Lyapunov theory and linear matrix inequalities (LMIs) tools, two main conditions are derived under which the fuzzy observer is designed. Finally, the procedure of the observer design is summarised and the effectiveness of the designed observer is demonstrated with a numerical example.