A fast linear consensus protocol on an asymmetric directed graph

In this paper, we generalize a fast linear consensus protocol design (Fastest Distributed Linear Averaging) from symmetric undirected graphs to asymmetric directed graphs. This design problem can be cast as a non-convex optimization. We propose a procedure to approximately solve this optimization problem using a sequence of semidefinite programs. Our procedure is guaranteed to generate a consensus protocol for a strongly connected graph that shows a faster convergence compared to the protocols from existing algorithms in our simulation.