Couple-group consensus of continuous-time multi-agent systems under Markovian switching topologies

This paper studies the couple-group consensus problem of multi-agent systems with general linear time-invariant dynamics. The interaction among agents is governed by a continuous-time homogeneous Markov process, whose state space corresponds to all the possible communication topologies. A linear consensus protocol is introduced to realize the couple-group consensus, where the agents in one subnetwork reach a consistent state while those in the other subnetwork reach another consistent state. When the agent dynamics is stabilizable, it is found that the couple-group consensus can be achieved under some mild algebraic and topological conditions of the inter-communication and intra-communication of agents in the two subnetworks. Appropriate consensus gain is designed and the speed to consensus is derived. Finally, three numerical examples are included to illustrate the obtained results.