In this paper, we investigate the consensus problem over communication networks where the communication channels are represented by stable LTI systems. We give sufficient conditions to reach consensus for our protocol and derive the consensus value which is function of the agents’ initial state, the network topology and the channel dynamics. We show that if the H1 norm of each channel filter is equal to its DC gain, the proposed protocol will solve the consensus problem. This result is interpreted in terms of consensus robustness to channel uncertainty and compared with another robustness condition for a different uncertainty class.