Distributed H_∞ control of multi-agent systems with directed networks

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.