Convergence analysis of discrete-time multi-agent systems based on sequential connectivity

It is well known that the jointly connectivity and sequential connectivity are two fundamental concepts in multi-agent systems. We discover that the jointly connectivity is equivalent to sequential connectivity if the communication topology has self-loops at each node. Based on the above result, the consensus of discrete-time multi-agent systems is then given under the condition of jointly connectivity by constructing a sequentially connected sequence. The above proof greatly simplified the former proofs.