Three-phase pulsewidth modulation (PWM) converters, specifically, voltage-source inverters (VSI), are possibly the most frequently used power converters for applications such as industrial motor control, robotics, air conditioning and ventilation, uninterruptible power supplies, electric vehicles, etc. With the introduction of standards on limiting harmonic pollution of electrical power distribution systems, three-phase PWM converters are being considered as prime candidates for interfacing high-power electronic equipment to power supply lines. In these applications, converters can provide input currents without distortion and with unity power factor. In this paper, the idea of using variable-structure system (VSS) control strategy of a boost rectifier in sliding mode is described. A new discrete-time control algorithm has been developed by combining VSS and Lyapunov design. It possesses all the good properties of the sliding mode and avoids the unnecessary discontinuity of the central input, thus eliminating chattering, which has been considered a serious obstacle to applications of VSS. A unified control approach for output DC voltage and input AC currents based on discrete-time sliding mode is developed. The reference tracking performance is demonstrated in terms of transient and steady-state characteristics by simulation and experimental results. The invariance and the robustness features of the proposed control method are verified by experiment in the presence of large uncertainty in parameters and external perturbations.