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In this paper, a robust leader-following consensus protocol for multi-agent systems (MASs) subject to faults in the information exchange and disturbance is presented. The problem under consideration is to guarantee the convergence of the agent trajectories to a leader agent when all the agent followers are under faults in the information exchange as smooth time-varying delays and disturbances. The main contribution in this paper is the design of a robust leader-following control through the Lyapunov approach and an optimal H ∞ criterion such that all agents follow a virtual leader agent despite faults in the information exchange and disturbances. Linear matrix inequalities (LMIs)-based conditions are obtained whose solution allows computing the robust controller gain. In order to show the effectiveness of the proposed approach, numerical examples are carried out comparing a state-of-the-art approach and the proposed strategy in a fleet of unmanned aerial vehicles (UAVs) subject to wind turbulence which are shown to achieve the formation control.INDEX TERMS Consensus, communication faults, leader-following consensus, multi-agent systems.