Distributed set membership estimation with time-varying graph topology

Distributed estimation schemes are increasingly popular these days. A distributed algorithm, specifically tailored to recursive set membership estimation problems, was recently proposed and analyzed for networks featuring a static topology. It was shown that the agents' estimates asymptotically converge to a common point lying in the intersection of all the agents' feasible sets. In this paper, by building on recent results on constrained consensus, we prove convergence in the more challenging scenario of networks with time-varying topology. It is shown that convergence is guaranteed if the sequence of graphs is jointly strongly connected over finite-length time intervals. Moreover, an asynchronous version of the proposed algorithm is presented, whose convergence can be deduced from the previously obtained results.