Convergence Rate of Consensus Algorithms with Multiplicative and Additive Noisy Measurements

Convergence rate analysis for consensus algorithms with noisy measurements has important applications in many distributive control and estimation problems. In particular, it determines whether a consensus-based time synchronization algorithm is convergent or not over networks with random bounded communication delays. In this paper, sufficient conditions in terms of topology digraphs and algorithm parameters are derived for quantifying convergence rate of the consensus algorithm with both multiplicative and additive noises.