Effect of bounded delay on convergence speed of distributed consensus algorithms

In this paper, we study distributed consensus algorithms in topology varying networks where there is communication delay between transmissions and receptions. In previous work, it is shown that the ultimate convergence of averaging based consensus algorithms is not affected by bounded delay. In the present work, we establish the same fact by showing that a finite power of the delay augmented system matrix is scrambling. Furthermore, we investigate the effect of bounded delay on convergence speed, and show by constructing certain topologies that delay does not always reduce convergence speed.