Optimal worst-case dynamic average consensus

We formulate a method for designing dynamic average consensus estimators with optimal worst-case asymptotic convergence rate over a large set of undirected graphs. The estimators achieve average consensus for constant inputs and are robust to both initialization errors and changes in network topology. The structure of a general class of polynomial linear protocols is characterized and used to find global optimal parameters using polynomial matrix inequalities (PMIs). For the case of the PI estimator, these conditions are converted into convex linear matrix inequalities (LMIs) and solved efficiently.