H∞ Fuzzy Filter for Nonlinear Singularly Perturbed Systems

This paper addresses the problem of designing an H∞ filter for a class of nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a fuzzy H∞ filter that guarantees the L2-gain from an exogenous input to a filter error to be less than or equal to a prescribed value. In order to alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard singularly perturbed nonlinear systems.