Effect of time delays on the convergence speed of consensus dynamics
We discuss consensus problems under time delays. The presence of time delays results in an inﬁnite-dimensional system rather than a system of ordinary differential equations. It has been shown that information transmission delays do not inﬂuence whether the system converges to a consensus value; however, further eﬀects of delays are unknown. We show that time delays in most graphs decreases the convergence speed; while somewhat surprisingly, they can improve convergence in certain special graphs. We discuss the structure of graphs for which such improvement is possible.