In this paper, we study the robust consensus problem for a set ofdiscrete-time linear agents to coordinate over an uncertain communicationnetwork, which is to achieve consensus against the transmission errors andnoises resulted from the information exchange between the agents. We model thenetwork by means of communication links subject to multiplicative stochasticuncertainties, which are susceptible to describing packet dropout, randomdelay, and fading phenomena. Different communication topologies, such asundirected graphs and leader-follower graphs, are considered. We derivesufficient conditions for robust consensus in the mean square sense. Thisresults unveil intrinsic constraints on consensus attainment imposed by thenetwork synchronizability, the unstable agent dynamics, and the channeluncertainty variances. Consensus protocols are designed based on the stateinformation transmitted over the uncertain channels, by solving a modifiedalgebraic Riccati equation.
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