Consensus over Stochastically Switching Directed Topologies

We consider average consensus algorithms executed over stochastically varying communication topologies that may be unbalanced. It is known that the state values will reach consensus, under fairly weak conditions. However, the consensus value is a random variable. We provide concentration bounds for the distance of the state vector from the consensus subspace and for the asymptotic distribution of the value to which the various nodes converge as they reach consensus. The results allow the analysis of average consensus over wireless communication networks with more realistic assumptions than before.

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