Distributed consensus of second-order multi-agent systems with uniquely sampled position data

Second-order consensus in multi-agent systems is discussed based on uniquely sampled position data. A distributed linear consensus protocol, where only out-dated and current sampled position data are utilized, is designed for each agent. It is revealed that second-order consensus in such a multi-agent system cannot be reached without any out-dated sampled position data in the proposed protocol. However, consensus can be achieved by appropriately choosing the sampling period and the coupling gains. To this aim, a necessary and sufficient condition with respect to the coupling gains, the sampling period, and the spectra of the Laplician matrix, is established for achieving consensus. Finally, effectiveness of the theoretical results is illustrated through numerical simulations.