Consensus of complex network systems and ergodicity of Markov chains

This study studies the consensus of multi-agent systems on time-varying network topologies. It is shown that this consensus reaching is equivalent to the corresponding weak ergodicity of the Markov process. A very mild sufficient condition of the consensus reaching that allows the communication among agents to be time-dependent and directed is obtained by estimating the Dobrushin coefficient of ergodicity. It is also shown that the notion of in-branching spanning tree plays a central role in the reaching of consensus. Moreover, sufficient conditions for (almost sure) consensus are presented for the case of time-varying networks.