Robust Mixed $l_{1}/H_{\infty}$ Filtering for Affine Fuzzy Systems With Measurement Errors

This paper investigates the robust filtering problem for a class of nonlinear systems described by affine fuzzy parts with norm-bounded uncertainties. The system outputs are chosen as the premise variables of fuzzy models, and their measured values are chosen as the premise variables and inputs of fuzzy filters. The measurement errors between the outputs of the plant and the inputs of the filter are considered, and as a result, the plant and the estimator cannot always evolve in the same region at the same time, especially in the neighborhoods of region boundaries. By using a piecewise Lyapunov function combined with S-procedure and adding slack matrix variables, a fuzzy-basis-dependent mixed I1/H∞ filter design method is obtained in the formulation of linear matrix inequalities, which allows for reducing the worst case peak output due to the measurement errors, and satisfying an H∞-norm constraint. In contrast to existing work, the proposed fuzzy-basis-dependent filter can guarantee a better H∞ performance and less computational burden. Finally, a numerical example illustrates the effectiveness of the proposed method.