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This paper introduces an extension of minimum variance beamforming that explicitly uses the a-priori uncertainty in the array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold; this uncertainty is modeled via an ellipsoid. We choose weights that minimize the total weighted power output of the array, subject to the constraint that the gain exceeds unity for all possible array responses in this ellipsoid. We show that the robust weights can be computed efficiently using Lagrange multiplier techniques. Numerical examples are presented.