LAUSR

Abstract In this paper, considering discrete-time average consensus with uniform constant time delays, we focus on the stability, the final consensus value and the convergence rate. Specifically, it is proven that average consensus is robust to time delays via a matrix theory-based approach. Then, the deviation of the final value from the average of the initial states is expressed explicitly. It is found that average consensus is only preserved in some special topologies, i.e., regular graphs. Finally, for the regular graph, it is proven that the convergence rate of average consensus decreases with time delays by comparing the second largest eigenvalues modulus (SLEM) of the update matrices.