  We study the performance of discrete-time consensus protocols in the presence
of additive noise. When the consensus dynamic corresponds to a reversible
Markov chain, we give an exact expression for a weighted version of
steady-state disagreement in terms of the stationary distribution and hitting
times in an underlying graph. We then show how this result can be used to
characterize the noise robustness of a class of protocols for formation control
in terms of the Kemeny constant of an underlying graph.

Optimization and Control;Distributed, Parallel, and Cluster Computing;Systems and Control;Probability