Finite Frequency $L_{2}{-}L_{\infty }$ Filtering of T-S Fuzzy Systems With Unknown Membership Functions
针对隶属函数未知的T-S模糊系统，定义了有限频域内的L2-L∞性能指标，并设计了变增益滤波器，仿真表明该方法优于全频域方法。
This paper is concerned with the problem of finite frequency L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for Takagi-Sugeno fuzzy systems with unknown membership functions. An L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index is first defined in finite frequency domain from the signal's point of view. By using matrix trace calculations, a new result based on L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis is derived in finite frequency range. Moreover, a design criterion of the desired finite frequency filter with varying gains is given in terms of a set of linear matrix inequalities and switching laws. It is shown that the proposed finite frequency filtering method can achieve better filtering performance than the existing full frequency ones. Finally, two simulation examples are introduced to verify the theoretical results.