This paper addresses the prescribed-instant consensus (PSIC) tracking problem of the leader-follower high-order multi-agent systems (MASs). Both cases of directed graphs and undirected connected graphs are considered. A Lyapunov-based sufficient condition for prescribed-instant stability of general single-loop systems is proposed. Based on the backstepping method, distributed control approaches are proposed to ensure consensus at the prescribed time instant. Consensus analyses are provided on the basis of Lyapunov stability theory and algebraic graph theory. Two numerical simulations are carried out which illustrates the validity of the proposed methods at the end.
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