Consensus in multi-agent systems with second-order dynamics and sampled position data

In this paper the problem of second-order consensus in multi-agent dynamical systems with sampled position data is addressed. Both the current and some sampled past position data are used to design a distributed linear consensus protocol with second-order dynamics. It turns out that sampled position data, especially the sampling period, is critical for such a multi-agent system to achieve second-order consensus under the given protocol. Then a necessary and sufficient condition for reaching consensus is derived, followed by a characterization of consensus regions. When the eigenvalues of the Laplacian matrix are all real-valued, the multi-agent system can achieve second-order consensus almost for any sampling period. The proposed theory is validated by computer simulations.