Distributed constrained consensus in the presence of unbalanced switching graphs and communication delays

In this paper, a constrained consensus problem is studied in unbalanced networks in the presence of communication delays. Here each agent needs to lie in a closed convex set while reaching a consensus. The communication graphs considered are directed, dynamically changing, and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length. The analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary. It is showed that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system. It is also showed that the communication delays do not affect the consensus stability and consensus is achieved even though the communication delays are arbitrary bounded.