  In this paper, we study the robust consensus problem for a set of
discrete-time linear agents to coordinate over an uncertain communication
network, which is to achieve consensus against the transmission errors and
noises resulted from the information exchange between the agents. We model the
network by means of communication links subject to multiplicative stochastic
uncertainties, which are susceptible to describing packet dropout, random
delay, and fading phenomena. Different communication topologies, such as
undirected graphs and leader-follower graphs, are considered. We derive
sufficient conditions for robust consensus in the mean square sense. This
results unveil intrinsic constraints on consensus attainment imposed by the
network synchronizability, the unstable agent dynamics, and the channel
uncertainty variances. Consensus protocols are designed based on the state
information transmitted over the uncertain channels, by solving a modified
algebraic Riccati equation.
