Average consensus on general digraphs

We study the average consensus problem of multiagent systems for general network topologies with unidirectional information flow. We propose a linear distributed algorithm which guarantees state averaging on arbitrary strongly connected digraphs. In particular, this graphical condition does not require that the network be balanced or symmetric, thereby extending the previous results in the literature. The novelty of our approach is the augmentation of an additional variable for each agent, called “surplus”, whose function is to locally record individual state updates. For convergence analysis, we employ graph-theoretic and nonnegative matrix tools, with the eigenvalue perturbation theory playing a crucial role.