Consensus stabilization of stochastic multi-agent system with Markovian switching topologies and stochastic communication noise

In this paper, we study stochastic consensus stabilization problems for a stochastic high-order multi-agent system with Markovian switching topologies and stochastic communication noise. By using the generalized Ito^ formula for the Markovian switching multi-agent system with stochastic communication noise, a state-feedback controller is constructed to ensure that the stochastic high-order multi-agent system reaches consensus in mean square sense when each agent's dynamics has unstable open-loop poles. A necessary and sufficient condition for the stochastic mean square consensus stabilization of the stochastic multi-agent system subject to Markovian switching topologies and additive disturbance is established under a distributed control protocol, i.e., the digraph is balanced and the union of the communication topology set contains a spanning tree. Numerical simulation is presented to demonstrate the theoretical analysis.