This paper treats the robust H-2 performance question of evaluating the rejection of continuous-time white noise, in the worst case over structured uncertainty in the system. A frequency domain convex condition for robust H-2 analysis is presented, with analogous properties as in the discrete-time case. In particular, necessary and sufficient results are obtained introducing a continuous-time version of the methodology of set descriptions of white noise. In addition, a state-space test in terms of linear matrix inequalities is developed for the robust H-2 problem in the case of constant uncertainty scalings, which apply to nonlinear or time-varying uncertainty. Thus the problem is rendered finite dimensional in the same situation in which robust H-infinity analysis is finite dimensional.