Consensus control for second-order multi-agent with time-delay on antagonistic networks

In this paper, we discuss consensus problems for antagonistic networks with double integrator dynamics. Two cases are analyzed: (1) undirected graphs with fixed topology on antagonistic networks; (2) undirected graphs with fixed topology and time-delay on antagonistic networks. For both cases, distributed consensus protocols are proposed, with sufficient and necessary conditions given. It is proved that the largest tolerable time-delay is only related to the largest eigenvalue of the graph Laplacian. Finally, simulations are provided to demonstrate the obtained theoretical results.

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