Sampled-data based average consensus of second-order integral multi-agent systems: Switching topologies and communication noises

A distributed sampled-data based protocol is proposed for the average consensus of second-order integral multi-agent systems under switching topologies and communication noises. Under the proposed protocol, it is proved that sufficient conditions for ensuring mean square average consensus are: the consensus gain satisfies the stochastic approximation type condition and the communication topology graph at each sampling instant is a balanced graph with a spanning tree. Moreover, if the consensus gain takes some particular forms, the proposed protocol can solve the almost sure average consensus problem as well. Compared with the previous work, the distinguished features of this paper lie in that: (1) a sampled-data based stochastic approximation type protocol is proposed for the consensus of second-order integral multi-agent systems; (2) both communication noises and switching topologies are simultaneously considered; and (3) average consensus can be reached not only in the mean square sense but also in the almost sure sense.