In this article, the fault detection (FD) filter design problem is addressed for discrete-time memristive neural networks with time delays. When constructing the system model, an event-triggered communication mechanism is investigated to reduce the communication burden and a fault weighting matrix function is adopted to improve the accuracy of the FD filter. Then, based on the Lyapunov functional theory, an augmented Lyapunov functional is constructed. By utilizing the summation inequality approach and the improved reciprocally convex combination method, an FD filter that guarantees the asymptotic stability and the prescribed $H_{\infty }$ performance level of the residual system is designed. Finally, numerical simulations are provided to illustrate the effectiveness of the presented results.

中文翻译：

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具有时间延迟的离散时间忆阻神经网络的事件触发故障检测滤波器设计

在本文中，针对具有时间延迟的离散时间忆阻神经网络解决了故障检测 (FD) 滤波器设计问题。在构建系统模型时，研究了一种事件触发的通信机制以减轻通信负担，并采用故障加权矩阵函数来提高FD滤波器的精度。然后，基于Lyapunov泛函理论，构造了一个增广Lyapunov泛函。利用求和不等式方法和改进的倒易凸组合方法，提出了一种保证渐近稳定性和规定的FD滤波器 $H_{\infty }$设计了剩余系统的性能水平。最后，提供数值模拟来说明所提出结果的有效性。