Average Consensus in Matrix-Weight-Balanced Digraphs

This paper investigates average consensus in first-order multi-agent systems where the interconnections are modelled by balanced digraphs with matrix weights. The paper first introduces the notion of a balanced directed graph for matrix weights. Then, it shows that the necessary and sufficient condition for the multi-agent system to achieve average consensus is that the matrix weights of its balanced digraph are positive definite. The Lyapunov analysis exploits a specific property of the mirror graph for a balanced graph. Simulations with holonomic robots in Gazebo verify the conditions for average consensus. Finally, formation control of a multi-agent system is shown as an application of the work presented.