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We study the average consensus problem of multi-agent systems for generalnetwork topologies with unidirectional information flow. We propose two(linear) distributed algorithms, deterministic and gossip, respectively for thecases where the inter-agent communication is synchronous and asynchronous. Ourcontribution is that in both cases, the developed algorithms guarantee stateaveraging on arbitrary strongly connected digraphs; in particular, thisgraphical condition does not require that the network be balanced or symmetric,thereby extending many previous results in the literature. The key novelty ofour approach is to augment an additional variable for each agent, called"surplus", whose function is to locally record individual state updates. Forconvergence analysis, we employ graph-theoretic and nonnegative matrix tools,with the eigenvalue perturbation theory playing a crucial role.

Average Consensus on General Strongly Connected Digraphs