Consensus Problem of Multi-Agent Systems with an Active Leader and Time Delay

In this paper, we consider the consensus problem of multi-agent systems with an active leader and variable interconnection topology. In our problem, the leader is active, that is, its states keep changing and may not be measured. To track such a leader, a neighbor-based control rule and state-estimation rule, both with time delay, are given for each autonomous agent. Then the tracking error is estimated. Particularly, it is proved that each agent can follow the leader if the (acceleration) input of the active leader is known.