A linear-quadratic output-feedback approach is given for designing digital servo-control systems of specified structure. The result is digital controllers that have a sensible structure based on classical control theory, in contrast to standard LQR design using state feedback plus an observer. The correct initial conditions for determining the LQ tracker output-feedback gains are not uniformly distributed as is traditionally assumed, but are shown to be explicitly given in terms of the step command magnitude. Both pole and zero placement are used to optimize the performance index. Arbitrary systems are treated, not only those with integrators in the forward paths, by adding a term to the performance index that weights the steady-state error. The approach works even if the system is non-minimum-phase. Necessary conditions are derived that may be used in a gradient-based routine to determine the optimal digital control gains. The approach does not rely on redesign of a continuous control system using techniques like the bilinear transformation, but uses direct discrete-time design. An aircraft digital command augmentation system is included as a sample design.