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In this study, the lth order (l ≥ 2) consensus problem for multi-agent systems is considered, which generalises the existing second-order consensus algorithm. A linear consensus protocol is proposed for solving such a consensus problem, which includes two parts: a feedback controller and interactions from the neighbours. A sufficient and necessary condition for consensus in high-order systems is obtained. As special cases, criteria for second- and third-order systems are given, in which the exact relationship between feedback gain and system parameters is established. Finally, numerical simulations are reported to illustrate the effectiveness of this protocol.