Consensus Over Ergodic Stationary Graph Processes
Coauthor(s): Ali Jadbabaie.
In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying
graphs of the network are generated by an ergodic and stationary random process.We prove that consensus algorithms converge almost surely, if and only if, the expected graph of the network contains a directed spanning tree. Our results contain the case of independent and identically distributed graph processes as a special case. We also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate.
Source: IEEE Transactions on Automatic Control
Tahbaz-Salehi, Alireza, and Ali Jadbabaie. "Consensus Over Ergodic Stationary Graph Processes." IEEE Transactions on Automatic Control 55, no. 1 (January 2010): 225-230.