Two protocols are presented,which can make agents reach consensus while achieving and preserving the desired formation in fixed topology with and without communication timedelay for multi-agent network.First,the protocol without considering the communication time-delay is presented,and by using Lyapunov stability theory,the sufficient condition of stability for this multi-agent system is presented.Further,considering the communication time-delay,the effectiveness of the protocol based on Lyapunov-Krasovskii function is demonstrated.The main contribution of the proposed protocols is that,as well as the velocity consensus is considered,the formation control is concerned for multi-agent systems described as the second-order equations.Finally,numerical examples are presented to illustrate the effectiveness of the proposed protocols. Two protocols are presented, which can make agents reach consensus while achieving and preserving the desired formation in fixed topology with and without communication time delay for multi-agent networks. First, the protocol without considering the communication time-delay is presented, and by using Lyapunov stability theory, the sufficient condition of stability for this multi-agent system is presented. Future, considering the communication time-delay, the effectiveness of the protocol based on Lyapunov-Krasovskii function is demonstrated. The main contribution of the proposed protocols is that, as well as the velocity consensus is considered, the formation control is concerned for multi-agent systems described as the second-order equations. Finally, numerical examples are presented to illustrate the effectiveness of the proposed protocols.