Cluster Consensus of Multi-agent Systems with Second Order Dynamics Over Matrix-weighted Graphs

Distributed cluster consensus problem for a set of agents with second order dynamics is considered here. In cluster consensus, agents within one cluster converge to a common value, and agents within different clusters converge to a different final value. It is shown that when the agents interact over a matrix weighted graph that is multi-partitioned and structurally balanced, cluster consensus is achieved. An additional cluster consensus scheme where agents update their states with respect to a dynamic common leader, is also developed. Under appropriate connectedness conditions, agent positions are shown to achieve cluster consensus around the leader position and the agent velocities are shown to converge to the leader velocity, asymptotically. Results are analytically shown using Lyapunov theory and are illustrated by numerical simulations.