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We are concerned with the consensus problems for networks of second-order agents, where each agent can only access the relative position information from its neighbours. We aim to find the largest tolerable input delay such that the system consensus can be reached. We introduce a protocol with time-delay and fixed topology. A sufficient and necessary condition is given to guarantee the consensus. By using eigenvector-eigenvalue method and frequency domain method, it is proved that the largest tolerable time-delay is only related to the eigenvalues of the graph Laplacian. And simulation results are also provided to demonstrate the effectiveness of our theoretical results.

Consensus of Second-Order Multiagent Systems with Fixed Topology and Time-Delay