Filtering for Takagi-Sugeno Fuzzy Systems with Norm-Bounded Uncertainties

We study the filter design problem for Takagi-Sugeno fuzzy systems which are subject to norm-bounded uncertainties in each subsystem. As we know that the Takagi-Sugeno fuzzy linear systems can be used to represent smooth nonlinear systems, the studied plants can also be uncertain complex systems. We suppose to design a filter with the order of the original system which is also dependent on the normalized fuzzy-weighting function; that is, the filter is also a Takagi-Sugeno fuzzy filter.With the augmentation technique, an uncertain filtering error system can be obtained and the systemmatrices in the filtering error system are reorganized into two categories (without uncertainties and with uncertainties). For the filtering error system, we have two objectives. (1) The first one is that the filtering error system should be robust stable; that is, the filtering error system is stable though there are uncertainties in the original system. (2) The second one is that the robust energy-to-peak performance should be guaranteed. With the well-known Finsler’s lemma, we provide the conditions for the robust energy-to-peak performance of the filtering error system in which three slack matrices are introduced. Finally, a numerical example is used to show the effectiveness of the proposed design methodology.