This paper investigates the leader-following consensus problem of Markov jump multi-agent systems affected by random denial-of-service attacks. A Markov jump process is used to describe the switching topologies caused by attacks, and the general transition probability matrix is employed which is considered as not completely available and contains some errors. Besides, with the help of the Lyapunov stability theory and linear matrix inequality technology, some sufficient conditions are established to make sure that the mixed $H_{\infty }$ and passive consensus can be achieved. Finally, a numerical example is given to illustrate the correctness and effectiveness of the proposed method.

本文研究了受随机拒绝服务攻击影响的马尔可夫跳跃多代理系统的领导者跟随共识问题。马尔可夫跳跃过程用于描述由攻击引起的切换拓扑，并采用一般转移概率矩阵，该矩阵被认为不完全可用且包含一些错误。此外，借助李亚普诺夫稳定性理论和线性矩阵不等式技术，建立了一些充分条件以确保混合$H_{\infty }$并且可以达成被动共识。最后给出数值例子说明所提方法的正确性和有效性。