An LMI approach to robust multimodel controller design is proposed. The fast output sampling control law considered here allows in theory to realize the effect of a robust state feedback gain simultaneously for a family of linear models. In practice, there are two reasons why exact realization of state feedback may not be desirable or even impossible: poor error dynamics, and noise sensitivity due to large output feedback gains. An LMI formulation of the design problem allows to approximate a robust state feedback design by fast output sampling, in a way that closeness to the original design can be traded against reducing these deteriorating effects. The proposed method is illustrated by a multivariable design example and experimental results.