This article addresses the issue of delay‐dependent H_∞ filtering design for TakagiŮSugeno fuzzy time‐varying delay systems using the input–output approach. A three‐term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function's (MF) time derivative, upper‐bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time‐derivative, the H_∞ full‐ and reduced‐order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.

中文翻译：

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Takagi-Sugeno模糊时变时滞系统的全阶和降阶H∞滤波：输入-输出方法

本文讨论的延迟依赖性的问题ħ _∞用于使用所述输入输出方法TakagiŮSugeno模糊时变延迟系统滤波设计。已使用三项近似模型将原始系统转换为两个相互连接的子系统。由于非二次Lyapunov–Krasovskii泛函需要处理隶属函数（MF）的时间导数，因此上限不等式已添加到获得的条件中。基于所述缩放的小增益定理，非二次李雅普诺夫-Krasovskii泛函的方法并考虑到MF时间导数，所述的界限ħ _∞设计全阶和降阶滤波器，然后根据线性矩阵不等式进行表述。最后，给出了说明性的例子来证明所提出的方法的有效性。