Robustness in Consensus Networks.

We consider the problem of robustness in large consensus networks that occurin many areas such as distributed optimization. Robustness, in this context, isthe scaling of performance measures, e.g. H2-norm, as a function of networkdimension. We provide a formal framework to quantify the relation between suchperformance scaling and the convergence speed of the network. Specifically, weprovide upper and lower bounds for the convergence speed in terms of robustnessand discuss how these bounds scale with the network topology. The maincontribution of this work is that we obtain tight bounds, that hold regardlessof network topology. The work here also encompasses some results in convergencetime analysis in previous literature.