Multi-agent consensus convergence analysis with infinitely jointly connected and directed communication graphs

In this paper, we investigate the connectivity conditions on consensus of discrete-time multi-agent systems with time-varying communication graph. We consider quite general switching communication topologies, whose length between the switching moments may tend to infinity with the well-known uniformly joint connectivity as its special case. We prove that the persistent graph of this network communication graph plays an important role in the agreement seeking, and give necessary and sufficient conditions for the global consensus.