Sufficient conditions on distributed averaging with compound noises and fixed topologies

In this paper, the distributed average consensus of discrete-time multi-agent networks is studied with compound noises and fixed topologies. Each agent updates its state through communication with neighbour agents. The communication model contains both additive and multiplicative noises. To attenuate the additive noises, the time-varying algorithm gain is introduced. By the algebraic graph theory, matrix theory and martingale convergence theory, we get the sufficient conditions for all agents' states converging to a common random variable in mean square and almost surely, whose expectation is right the average of the initial values of all agents, and whose variance is bounded by a quantity related to the maximal weight and in-degree, the time-varying algorithm gain, the number of agents, the agents' initial values, the second-order moment and the intensity coefficients of the noises.