Consensus for discrete multi-agent systems with bounded delays under static and randomly switching topologies

The consensus problem for multi-agent systems with time-varying communication and input delays and dynamically changing communication topology is investigated in this paper based on graph theory. The condition for solving the consensus problem is that the graph of the communication topology is repeatedly jointly rooted or the union of the graph is rooted. The result is extended to randomly switching topology environments. Some examples are presented to illustrate the proposed consensus protocols.