The scaled bipartite consensus of second-order multi-agent systems is investigated in this paper. The internal delay and distributed delay are also considered in the dynamic model of each agent, in which the delays can be time-varying and large. The communication topology among agents is assumed to be directed and structurally balanced. On one hand, in order to guarantee scaled bipartite consensus of second-order multi-agent systems, an adaptive periodically intermittent control protocol is applied. On the other hand, some consensus criteria in the form of matrix inequalities are obtained by using Jensen inequality, Lyapunov stability theory and graph theory. Finally, a numerical simulation example is given to demonstrate the feasibility of theoretical results.

本文研究了二阶多智能体系统的缩放二部共识。每个代理的动态模型中也考虑了内部延迟和分布式延迟，其中延迟可以是时变的和大的。代理之间的通信拓扑被假定为定向和结构平衡的。一方面，为了保证二阶多智能体系统的规模化二方共识，应用了自适应周期性间歇控制协议。另一方面，利用Jensen不等式、Lyapunov稳定性理论和图论，得到了一些以矩阵不等式形式存在的共识准则。最后通过数值模拟实例验证了理论结果的可行性。