On the Continuous-time Consensus Problems with Markovian Switching

Abstract—In this paper, we study the linear distributed asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. A finite state Markov process dominates each topology corresponding to a state of the process. We address both the cases where the dynamics of the agents is expressed in continuous and discrete time. As long as the consensus matrices are doubly stochastic, convergence to average consensus can be shown to be achieved in the mean square and almost sure sense. A necessary and sufficient condition is the graph resulted from the union of graphs corresponding to the states of the Markov process contains a spanning tree