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This paper considers the consensus problems for both continuous- and discrete-time linear multi-agent systems with directed communication topologies. Distributed reduced-order observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct a reduced-order protocol, under which a continuous-time multi-agent system whose communication topology contains a directed spanning tree can reach consensus. This algorithm has a favorable decoupling property. In light of the modified algebraic Riccati equation, an algorithm is then given to construct a reduced-order protocol for the discrete-time case.