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This paper studies a mean square average consensus of general linear discrete-time time-invariant multi-agent systems with communication noises.A distributed protocol,which is composed of the agent’s own state feedback and the relative states between the agent and its neighbors,is proposed.A time-varying consensus gain is applied to attenuate the effect of noises.A polynomial,namely “parameter polynomial”,is constructed in such a way that its coefficients are the paraments in the control gain vector of the proposed protocol.It turns out that the parameter polynomial plays an important role in the consensus analysis of linear multi-agent systems.It is proved that under the proposed protocol the necessary and sufficient conditions for ensuring the mean square average consensus are: the communication topology graph is balanced and strongly connected; the consensus gain satisfies the approximation-type conditions; and all roots of the parameter polynomial are in the unit circle.