On H∞ Filtering for Discrete-Time Takagi–Sugeno Fuzzy Systems

In this paper, we present a new design method for the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">H∞</tex></formula> filtering of discrete-time Takagi–Sugeno (TS) fuzzy systems. The parameters of the filter are assumed to be linearly dependent on the normalized fuzzy weighting functions. By using an augmentation technique, the design parameters are incorporated into a filtering error system. In order to derive less-conservative results and reduce the filtering error, a new condition is established to ensure the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">H∞</tex></formula> performance of the filtering error system. By introducing more slack matrices, the solution set of the filter parameters is extended. By using a partitioning technique, a design method for the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">H∞</tex></formula> filter is proposed in terms of linear matrix inequalities (LMIs). An example demonstrates the improvement of the proposed design method over an existing approach.