If system performance can be adequately measured by a quadratic function of the error, it is possible to present a single optimum design procedure that encompasses almost all linear, sampled-data control problems of interest. This development includes both random and deterministic inputs, the random parameter problem, and a general time-varying system. The results are in the form of iterative equations which specify the optimum linear feedback coefficients. The method constitutes a generalization of the work by Kalman, Koepcke, Bellman, and others, and presumes the availability of a digital computer to solve the final equations.