L1/H∞ Filter Design for Affine Fuzzy Systems with Imperfect Premise Matching

This paper addresses the robust filtering problem for a class of continuous-time nonlinear systems described by affine fuzzy models. The system outputs are chosen as premise variables of the fuzzy model, and their measured values are chosen as premise variables and inputs of the fuzzy filter. Performance requirements of the augmented system are stated as fuzzy summations, related to Lyapunov function. Different from the existing results, the influence of measurement errors on premise variables is considered, consequently, the nice characteristic given by the perfect premise matching cannot be used for the filter design. According to the introduction of slack matrices, relaxed linear matrix inequality (LMI)-based L
1
/H
∞
fuzzy filter design conditions are obtained using Lyapunov-based approach, which consider the information of the membership functions and measurement errors. Finally, a numerical example is provided to show the merits and effectiveness of the proposed approach.