Abstract: This paper considers the consensus problem of multi-agent systems with an active leader and time-varying delay. In our problem, the velocity of the leader can not be measured precisely. To track such a leader, a decentralized state-estimation rule is constructed for each agent, which is used to design local controllers. Due to the interconnection delays, both neighbor-based control rules and stat-estimation rules involve time-varying delays. Moreover, with the directed (fixed or variable) interconnection topologies described by digraphs, the leader-following errors are estimated. Particularly, it is proved that each agent can track the leader if th input of the active leader is precisely known.

Key words: multi-agent systems, consensus, active leader, time delay, digrah