This paper focuses on the design of $H_{\infty }$ filter for a class of discrete-time networked systems. Given that the network communication resources are becoming limited with the ever-increasing network traffic, an adaptive event-triggered mechanism (AETM) is adopted for the systems to mitigate the pressure of network bandwidth. The considered discrete-time networked systems are envisioned to suffer from both Deception attacks and denial-of-service (DoS) attacks, thereby a novel hybrid cyber attacks model is firstly constructed to integrate the two kinds of attacks. Then, a filtering error system model is established for the discrete-time networked systems under AETM and hybrid cyber attacks. Based on the constructed model, the sufficient conditions that guaranteeing the asymptotic stability and $H_{\infty }$ performance of the concerned filtering error system are analyzed based on Lyapunov–Krasovskii stability theory. Furthermore, the corresponding parameters of the designed filter are derived by solving a set of linear matrix inequalities (LMIs). The effectiveness of the designed filter is finally demonstrated by conducting a numerical example.

本文着重于设计 $H_{\infty }$一类离散时间网络系统的过滤器。鉴于网络通信资源随着网络流量的不断增加而变得有限，系统采用自适应事件触发机制（AETM）来缓解网络带宽压力。设想所考虑的离散时间网络系统同时遭受欺骗攻击和拒绝服务（DoS）攻击，因此首先构建了一种新颖的混合网络攻击模型来集成这两种攻击。然后，针对AETM和混合网络攻击下的离散时间网络系统建立过滤误差系统模型。基于所构建的模型，保证渐近稳定性的充分条件和$H_{\infty }$基于Lyapunov-Krasovskii稳定性理论分析了有关滤波误差系统的性能。此外，设计滤波器的相应参数是通过求解一组线性矩阵不等式 (LMI) 得出的。最后通过数值例子证明了所设计滤波器的有效性。