Consensus over networks with dynamic channels

In this paper, we investigate the consensus problem over communication networks where the communication channels are represented by stable Linear Time Invariant (LTI) systems. We give the necessary and sufficient condition to reach consensus under our protocol and show that the consensus value is not only determined by the agents' initial states and the network topology but also by the channels' dynamics. We further show that if the H∞ norm of each channel filter is equal to its DC gain, the extended 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.