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This paper considers both synchronous and asynchronous consensus algorithms with noisy measurements. For stochastic approximation based consensus algorithms, the existing convergence analysis with dynamic topologies heavily relies on quadratic Lyapunov functions, whose existence, however, may be difficult to ensure for switching directed graphs. Our main contribution is to introduce a new analytical approach. We first show a fundamental role of ergodic backward products for mean squaredoi:10.1109/tac.2012.2199149 fatcat:7cqsrvchefg43n26zmmo3g2yfm