This thesis describes work on the selection of the optimal control criterion weighting matrices, based on multivariable root loci and frequency domain properties. The case with a crossproduct weighting term in the cost function is examined and a design algorithm is proposed. The frequency domain solution to the finite time optimal control problem for discrete time systems is described and controller expressions in closed loop form are obtained for the regulation and tracking problems. The design of a strip shape control system for a Sendzimir cold rolling steel mill is described and problems of implementation are discussed. Finally, a detailed comparison between an optimal and a multivariable frequency domain design for a dynamic ship positioning system is presented. The effects of using Kalman filters for state estimate feedback in non-optimal systems is discussed.