The problems of prescribed-time leader-following consensus and prescribed-time containment control for double-integrator multiagent systems (MASs) with only position measurements are investigated in this paper. An observer-based prescribed-time control protocol is proposed, in which the two groups of observers for estimating the consensus errors of each follower both converge to zero within a specified time. Furthermore, the proposed controller only relies on its own observers and does not need to obtain the data from observers embedded in its neighbor nodes. The sufficient conditions for the MASs to achieve the defined prescribed-time consensus and to fulfill the goal of prescribed-time containment control are, respectively, given. The effectiveness of the proposed control protocol is further verified by computer simulations.
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