Passive filtering of neural networks with time-invariant delay and quantized output is considered. A criterion on the passivity of a filtering error system is proposed by means of the Lyapunov–Krasovskii functional and the Bessel–Legendre inequality. Based on the criterion, a design approach for desired passive filters is developed in terms of the feasible solution of a set of linear matrix inequalities. Then, analyses and syntheses are extended to the time-variant delay situation using the reciprocally convex combination inequality. Finally, a numerical example with simulations is used to illustrate the applicability and reduced conservatism of the present passive filter design approaches.

中文翻译：

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具有量化输出的时滞神经网络的无源滤波器的设计

考虑了具有时不变延迟和量化输出的神经网络的无源滤波。利用Lyapunov–Krasovskii泛函和Bessel–Legendre不等式，提出了过滤误差系统无源性的标准。基于该准则，根据一组线性矩阵不等式的可行解，开发了一种用于所需无源滤波器的设计方法。然后，利用双向凸组合不等式将分析和合成扩展到时变时滞情况。最后，通过一个带有仿真的数值示例来说明当前无源滤波器设计方法的适用性和降低的保守性。