This paper discusses the prescribed-time leader-follower consensus and containment control problems for a class of nonlinear multi-agent systems with external disturbances. First, an event-triggered control protocol with sign function is proposed, which can ensure that all agents achieve consensus within a prescribed time. Second, as the sliding mode control has the advantage of good robustness to external disturbances, an improved event-triggered control protocol is designed by using the integral sliding mode control method and some sufficient conditions are derived for achieving the prescribed-time leader-follower consensus. Moreover, the prescribed-time containment control problem for multi-agent systems with multiple leaders is investigated by using the event-triggered control strategy. It is shown that Zeno behavior can be excluded in the above consensus issues by choosing parameters appropriately. Finally, several numerical examples are given to demonstrate the effectiveness and reliability of the proposed approaches.
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