Consensus control of multi-agent systems with delays

This paper concerns the consensus problem of linear time-invariant multi-agent systems (MASs) with multiple state delays and communicate delays. Consensus control is widely applied in spacecraft formation, sensor networks, robotic manipulators, autonomous vehicles, and others. By introducing a linear transformation, the consensus problem of the delayed MAS under an undirected network was converted into a robust asymptotic stability problem associated with the eigenvalues of the normalized Laplacian matrix of the network. By means of the argument principle and optimization technologies, a numerical controller design method was presented for the delayed MAS to reach consensus. The effectiveness of the proposed approach was illustrated by some numerical examples. The proposed approach may be applied to multi-agent systems with distributed delays.