A generalized LQ-control problem, which treats a mixed attenuation of stored disturbance and initial state uncertainty, is discussed in the infinite-horizon time setting. The posed problem covers a part of predictive control problems and enables one to deal with the LQ optimal preview servocontroller design. For the generalized LQ problem, we first derive an optimal preview control which minimizes the LQ cost functional and provide some interpretations on the structure of resulting control law. We then analyze worst case initial uncertainties, i.e., those of initial state and the shape of stored disturbance, which maximize the cost functional of the resulting closed-loop system.