Abstract This paper studies the distributed H∞ control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞ controllers are proposed. The concept of an H∞ performance region is extended to the directed graph situation. Then the results are used to solve the leader-follower H∞ consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.
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