This paper proposes second-order consensus protocols and gives a measure of the robustness of the protocols to the time-delays existing in the dynamics of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states achieve second-order consensus as-ymptotically for appropriate time-delay if the topology of the net-work is connected. Particularly, a nonconservative upper bound on the fixed time-delay that can be tolerated is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which makes the pro-posed protocols scalable. It reduces the complexity of connections among agents significantly. Simulation results are provided to verify the effectiveness of the theoretical results for second-order consensus in networks in the presence of time-delays existing in the dynamics of agents.
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