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This paper studies the consensus control of linear multi-agent systems with optimal performance index on directed communication topologies. The consensus control protocols relying on the relative information between the agent and its neighbours are presented, and both the leaderless and leader-following cases are investigated. The global optimization of performance index is achieved with the presented control protocols by solving the algebraic Riccati equation (ARE), and the ARE can be solved without knowing the global information of communication topologies. The numerical examples are finally reported to illustrate the efficiency of the proposed protocols.