Discrete Average Consensus with Bounded Noise

This paper investigates the problem of discrete average consensus in the presence of bounded noise. Different from many existing works which mainly deal with noise with zero mean and bounded covariance, we consider the noise with bounded absolute value which is more practical in many applications. We first derive the necessary condition for the convergence of consensus under bounded noise. We then further obtain the sufficient condition under which the average consensus is guaranteed to converge. Under the same condition, we also derive the analytical bound for quantifying the effect of bounded noise on the converging value. For a more general case where the average consensus may not converge, we adopt the max-min distance to evaluate the network performance, and provide an analytical upper bound based on the network structure and the noise bound. Extensive simulations demonstrate the effectiveness of our results.