This paper presents a three-dimensional (3-D) space vector pulse width modulation (SVPWM) technique via a 4 x 4 orthonormal transformation matrix that has been used as a new approach in controlling a three-phase four-leg voltage source inverter (VSI). A fully optimal digital control scheme for the closed-loop regulation of the three-phase four-leg VSI has been used to synthesize a sinusoidal waveform with the help of the proposed method. Discrete-time modelling of each phase has been obtained independently in abc reference frame, and its optimal controller has been designed using a predefined performance index. A DSP-based controlled three-phase four-leg prototype VSI has been designed to verify the proposed discrete time modelling and the control scheme. The simulations and the real-time experiments show that satisfactory results have been obtained for the modelling of the three-phase four-leg VSI in abc reference frame and the 3-D SVPWM technique via 4 x 4 orthonormal transformation matrix at 20 kHz switching frequency.