A novel approach for the design of a discrete-time sliding mode controller is presented using a singular LQR-approach. The weighting of the control signal is set to zero and dead-beat behaviour for the sliding mode reaching dynamics is achieved. By analogy with continuous-time sliding mode control, the reaching dynamics are modified when the states are a significant distance away from the sliding surface to avoid any high magnitude control action due to the partial dead-beat approach. The control law also takes into account constraints on the actuator amplitudes and a stability analysis is presented using a discrete-time version of the Popov criterion.