Observer design for a discrete-time T-S fuzzy system with uncertainties

This paper aims to design an observer for a discrete time Takagi-Sugeno (T-S) fuzzy system in presence of uncertain terms. Due to these uncertainties, it is difficult to design an observer such that the state estimation errors converge to zero. Even some previous literatures have designed the observer, but their observer works well only under the conditions of bounded uncertainty. In order to overcome these drawbacks, the proposed method converts the uncertainties into the form of unknown inputs and applies the unknown-input method to the T-S fuzzy system such that the observer is designed to guarantee the estimation error approaching to zero asymptotically. In addition, the Lyapunov theory and Linear Matrix Inequality (LMI) tools are used for the parameters synthesis of the observer. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.