Observer Design for Uncertain T-S Fuzzy System with Multiple Output Matrices and Unmeasurable Premise Variables

This paper proposes a method based on unknown input method to synthesize an observer for uncertain Takagi-Sugeno fuzzy system with multiple output matrices where the upper bound constraint of uncertainties are not known either. Firstly, the mathematic transformation is employed to transform the conventional T-S fuzzy system into new form. Secondly, the unknown input method is applied to eliminate the impacts of uncertainties and make estimation error converge to zero. Additionally, the unmeasurable premise variables are studied in this paper as well. Based on the Lyapunov theory and Linear Matrix Inequality technique, the main theorems for synthesizing observer are derived. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed method.