This paper investigates asynchronous mixed passivity and \(H\infty \) filter design for fuzzy jump systems with time-varying delays. Firstly, new time delay-dependent stability conditions for the fuzzy Markovian jump systems are obtained by constructing a mode-dependent Lyapunov functional and introducing free weight matrices technique. Secondly, the asynchronous filter is designed via linear matrix inequalities, which can ensure stochastic stability and the mixed passivity and \(H\infty \) performance of the augmented Markovian jump filtering error system. A numerical example and a single-link robot arm are utilized to show the effectiveness of the method.

本文研究了具有时变时滞的模糊跳跃系统的异步混合无源和\（H \ infty \）滤波器设计。首先，通过构造依赖于模式的Lyapunov泛函并引入自由权矩阵技术，获得了模糊马尔科夫跳跃系统的新的时滞依赖稳定条件。其次，通过线性矩阵不等式设计异步滤波器，可以保证扩展的马尔可夫跳跃滤波误差系统的随机稳定性以及混合无源性和\（H \ infty \）性能。通过数值算例和单连杆机械臂来说明该方法的有效性。