This paper deals with the problem of average consensus of a set of time-varying reference signals in a distributed manner. We propose a new class of discrete time algorithms that are able to track the average of the signals with an arbitrarily small steady-state error and with robustness to initialization errors. We provide bounds on the maximum step size allowed to ensure convergence to the consensus with error below the desired one. In addition, for certain classes of reference inputs, the proposed algorithms allow arbitrarily large step size, an important issue in real networks, where there are constraints in the communication rate between the nodes. The robustness to initialization errors is achieved by introducing a time-varying sequence of damping factors that mitigates past errors. Convergence properties are shown by the decomposition of the algorithms into sequences of static consensus processes. Finally, simulation results corroborate the theoretical contributions of the paper. (C) 2014 Elsevier Ltd. All rights reserved.