Robust Consensus of Discrete-time Linear Agents over Deterministic Uncertain Channels

In this paper, we study the robust consensus problem for a group of linear discrete-time agents to coordinate over an uncertain communication network, which is to achieve consensus against transmission errors and noises. We model the network by communication links subject to deterministic uncertainties, which can be either an additive perturbation described by some unknown transfer function or a norm bounded uncertainty. We show that the robust consensus problem with undirected communication topologies is equivalent to the simultaneous H-infinity control problem for a set of low-dimensional subsystems. We derive a necessary condition for the existence of a protocol achieving robust consensus. That is, the upper bound of the uncertainties is less than the inverse of the Mahler measure of the agents. Sufficient conditions in terms of linear matrix inequalities are further presented to design the robust consensus protocols.