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 us to deal with LQ optimal preview servocontroller design. For the generalized LQ-problem, we first derive an optimal preview control which minimizes the LQ cost functional and pro,ide some interpretations on the structure of resulting control law. Then we analyze worst case initial uncertainties, i.e., those of initial state and the shape of stored disturbance, which maximize the cost functional of resulting closed-loop system.