This paper considers consensus problems with delayed noisy measurements, and stochastic approximation is used to achieve mean square consensus. For stochastic approximation based consensus algorithms with switching topologies, the existing convergence analysis heavily relies on quadratic Lyapunov functions, whose existence may be difficult to guarantee for switching digraphs. The main contribution of this paper is to introduce a new approach for proving convergence. This is achieved by obtaining ergodicity results for backward products of degenerating stochastic matrices via a discrete time dynamical system approach. Our approach does not require the double stochasticity condition typically assumed for the existence of a quadratic Lyapunov function.
2010 49th IEEE Conference on Decision and Control, CDC 2010
School of Mathematics and Statistics

Huang, M. (2010). Stochastic approximation for consensus with general time-varying weight matrices. Presented at the 2010 49th IEEE Conference on Decision and Control, CDC 2010. doi:10.1109/CDC.2010.5717234