Consensus Problems with Directed Markovian Communication Patterns

This paper is a continuation of our previous work and discusses the consensus problem for a network of dynamic agents with directed information flows and random switching topologies. The switching is determined by a Markov chain, each topology corresponding to a state of the Markov chain. We show that in order to achieve consensus almost surely and from any initial state, each union of graphs from the sets of graphs corresponding to the closed positive recurrent sets of states of the Markov chain must have a spanning tree. The analysis relies on tools from matrix theory, Markovian jump linear systems theory and random process theory. The distinctive feature of this work is addressing the consensus problem with “Markovian switching” topologies.