Optimal discrete-time control of linear systems has been presented already. There are some difficulties to design an optimal discrete-time control of robot manipulator since the robot manipulator is highly nonlinear and uncertain. This paper presents a novel robust optimal discrete-time control of electrically driven robot manipulators for performing repetitive tasks. The robot performs repetitive tasks by tracking a periodic trajectory. The proposed controller includes a discrete linear quadratic controller and a time-delay controller. To apply the discrete linear quadratic controller, a novel nominal model is obtained for the robotic system which is discrete, linear, and time-invariant. Then, nonlinearities and uncertainties of the robotic system are compensated by the robust time-delay controller. The proposed control law is verified by stability analysis and its effectiveness is illustrated by simulations. Recently, time-optimal and minimum-norm discrete repetitive control of robot manipulators has been proposed. Compared with it, the proposed control has an advantage of being free from manipulator dynamics, thus it is simpler, more robust, and less computational with smoother control efforts.