Stochastic Double Array Analysis and Convergence of Consensus Algorithms with Noisy Measurements

This paper considers consensus-seeking of networked agents in an uncertain environment where each agent has noisy measurements of its neighbors' states. We propose stochastic approximation type algorithms with a decreasing step size. We first establish consensus results in a two-agent model via a stochastic double array analysis. Next, we generalize the analysis to a class of well studied symmetric models and obtain consensus results.