Consensus with noisy information

This paper studies convergence and convergence rate of consensus algorithms with multiplicatively and additively noisy information over networks described by time-varying directed graphs. The main difference between the problem studied in this paper and the existing results in the literature is that the multiplicative noises are introduced directly by neighboring states instead of relative states, and hence, the perturbation matrix does not have zero row sums. Under the assumption that the noises are polynomially decaying, sufficient conditions in terms of connectedness measure of topology digraphs and algorithm parameters are derived for ensuring the convergence of the consensus algorithm, and convergence rate of the algorithm is also quantified.