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 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.
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