In this article, the problem of delay‐dependent dissipative filter design is studied for discrete‐time interval type‐2 (IT‐2) fuzzy singular systems with both external disturbance and mixed delays. Two kinds of delays are considered, namely time‐varying discrete delays and infinite distributed delays. First, considering the uncertainties in the membership functions, the nonlinear singular system and the filter are modeled by the IT‐2 fuzzy systems. Then, based on new matrix inequalities dealing with the mixed delays, a new delay‐dependent criterion is proposed to ensure the IT‐2 fuzzy filtering error system is to be admissible with strictly dissipative performance. The filter parameters are characterised by the solution of linear matrix inequalities (LMIs). The feasibility of these results are verified by a numerical example.

中文翻译：

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具有混合时滞的离散时间间隔2型模糊奇异系统的耗散滤波器设计

在本文中，研究了具有外部干扰和混合时滞的离散时间间隔2型（IT-2）模糊奇异系统的时滞相关耗散滤波器设计问题。考虑了两种延迟，即时变离散延迟和无限分布式延迟。首先，考虑隶属函数的不确定性，非线性奇异系统和滤波器由IT-2模糊系统建模。然后，基于处理混合延迟的新矩阵不等式，提出了一个新的依赖于延迟的准则，以确保IT-2模糊滤波误差系统以严格耗散的性能被接受。滤波器参数的特征在于线性矩阵不等式（LMI）的解。通过数值例子验证了这些结果的可行性。