On the effect of non-uniform transmission delays in distributed consensus

This paper investigates the performance of averaging based distributed consensus algorithms in topology varying networks with existing non-uniform transmission delays. A finite power of the delay augmented system matrix is shown to be scrambling which confirms that non-uniform bounded delay does not affect the ultimate convergence of the distributed iterative algorithms considered in this paper. The effect of bounded delay on convergence speed is also investigated, and it is shown via some well-known topologies that delay does not always reduce convergence speed.