Consensus of multi-agent systems with stochastic switching topology

This paper studies the mean square consentability problem for a network of double-integrator agents with stochastic switching topology. It is proved that in Markovian switching topologies, the network is mean square consentable under linear consensus protocol if and only if the union of graphs in the switching topology set has a globally reachable node. A necessary and sufficient condition of the mean square consensus is obtained. Finally, an LMI approach to the design of the consensus protocol is presented. Numerical simulations are given to illustrate the theoretic results.