An approach is presented to formulating the optimization problem of linear discrete-time systems in the presence of both waveform-type and noise-type disturbances. In addition, the plant output measurements are allowed to be corrupted by additive noise. It is shown that the optimal control, which minimizes the specified performance index and ensures that all closed-loop poles lie inside a circular region within a unit circle, can utilize the energy stored in waveform-type disturbance. An illustrative example is provided and simulation results are included to demonstrate the effectiveness of the presented approach.