The multi-functional converter system (MFCS) is a special topology of three-phase AC motor drives, which inherently integrates a DC-voltage regulation function. Firstly, in order to explain the mechanism of the MFCS, an average model is derived. An equivalent circuit is developed, which explicitly reveals that the MFCS is equivalent to a cascaded DC/DC converter-DC motor drive system. Secondly, the inverter's mean duty-cycle is identified as an independent control degree of freedom for the DC-bus voltage. Then, the influence of pulse width modulation (PWM) on the DC-bus voltage is studied. It concludes that space vector PWM is invalid for the MFCS. To address this problem, the zero-sequence voltage injection PWM (ZSVIPWM) is proposed and actually sinusoidal PWM is a special case of the ZSVIPWM. Thirdly, an overall control strategy is proposed for the MFCS, which includes not only the vector control for the motor but also a closed-loop control for the DC-bus voltage. Finally, comparative experiments with the standard topology are carried out on a permanent magnet synchronous machine prototype to verify these theoretical analyses and the control strategy.