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This paper presents a robust observer-based leader-following consensus control for multi-agent systems subject to external disturbances. The stability and robustness to external disturbances are addressed through the Lyapunov approach and an optimal H criterion. It is shown that the design conditions for a correct convergence of the estimated states and consensus control can be expressed in a set of linear matrix inequalities whose solution allows computing the observer and controller gain matrices. In order to show the effectiveness of the proposed strategy, numerical examples are carried out to solve the formation control problem of a fleet of unmanned aerial vehicles (UAVs) under the effect of wind turbulence.