Second-order consensus in multi-agent dynamical systems with sampled data

This paper studies second-order consensus in multi-agent dynamical systems with sampled position and velocity data. A distributed linear consensus protocol with second-order dynamics is designed, where both sampled position and velocity data are utilized. It is found that second-order consensus in such a multi-agent system can be achieved by appropriately choosing the sampling period which depends on the control gains and spectra of the Laplacian matrix. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. Then, second-order consensus in delayed undirected networks with sampled position and velocity data is discussed. A necessary and sufficient condition is also given, by which appropriate sampling period can be chosen to achieve the consensus. Finally, simulation examples are given to verify and illustrate the theoretical analysis.