This paper presents a frequency domain resilient consensus problem of time-delayed multi-agent systems (MASs) under attacks. An internal model principle-based attack, a kind of network attack, is firstly analyzed and modeled in frequency domain. Then, a Quasi-$H_{\infty }$ robust controller is designed for resilient consensus of the MAS with the help of an internal model controller. This scheme is different from the existing works in the sense that the attacker may inject an attacking signal on the node of an agent instead of a communication link. It is also novel because it can eliminate the impacts of attack without excluding compromised nodes and restricting the number of compromised nodes. The proposed control scheme is applied to a linear delayed MAS with single-input single-output agents and then transformed into multi-input and multi-output agents. An innovative approach is employed for the tuning of the proposed controller to track the performance of the MAS and its robustness. Some necessary and sufficient conditions are extracted using Pade$\stackrel{́}{}$ approximation and graph theory to minimize the impacts of time delay and attacks simultaneously. The results are extended for resilient consensus of the MAS under non-internal model principle-based attack. The simulation results are presented to demonstrate the validity of the proposed control strategy.

本文提出了时延多智能体系统（MAS）在攻击下的频域弹性共识问题。首先在频域分析和建模了基于内部模型原理的攻击，一种网络攻击。然后，一个准$H_{\infty }$鲁棒控制器旨在借助内部模型控制器实现 MAS 的弹性共识。该方案与现有工作的不同之处在于攻击者可能会在代理节点而不是通信链路上注入攻击信号。它也是新颖的，因为它可以消除攻击的影响，而无需排除受损节点并限制受损节点的数量。所提出的控制方案应用于具有单输入单输出代理的线性延迟 MAS，然后转换为多输入和多输出代理。采用一种创新方法对所提出的控制器进行调整，以跟踪 MAS 的性能及其鲁棒性。使用 Pade 提取一些充要条件$\stackrel{́}{}$近似和图论同时最小化时间延迟和攻击的影响。在非内部模型基于原则的攻击下，结果被扩展为 MAS 的弹性共识。仿真结果展示了所提出的控制策略的有效性。