Step size analysis in discrete-time dynamic average consensus

This paper deals with the problem of reaching the average consensus of a set of time-varying reference signals in a distributed manner. We analyze the approach initially presented in [1], giving an alternative proof of convergence which leads to larger, more realistic bounds on the step sizes that guarantee a steady-state error upper-bounded by a given constant. The interest of the new results appear when the algorithm is used in real networks, where there are constraints in the communication rate between the nodes. We derive the bounds for the cases of fixed and time-varying communication topologies, as well as for different orders of the algorithm. We demonstrate that our bounds always allow substantially bigger step sizes than those in [1], independently of the number of nodes or the topology. Moreover, for a fixed step size and steady-state error, we show how there is a corresponding algorithm that can guarantee that the error is no larger than the desired one, using that step size. Finally, simulation results corroborate the theoretical findings of the paper.