Based on the second-order neighbors' information, consensus algorithm was proposed to accelerate the consensus convergence speed for the average consensus problem of multi-agent systems. Meanwhile, the event-based control method was used in the design of consensus algorithm in order to reduce the number of communications in the systems. Firstly, under a fixed topology network, we looked at speeding up the consensus convergence by getting the multiagent systems to apply information to their second-order neig...