A control approach for three-phase four-leg LC-filtered voltage source inverters (VSIs) is proposed for an uninterruptible power supply (UPS) application. A filter inductor in the fourth (neutral) leg of the VSI is considered to enhance the output voltage quality when feeding different types of loads in such a system. The proposed approach is based on the modelling of UPS VSI system in the dq0 synchronous frame. First, the switching functions of the inverter under study are extracted from the achieved system model. Afterward, the control approach is developed by introducing a virtual time constant, which simultaneously affects the system's damping ratio, and a virtual undamped natural frequency in the switching functions. It offers flexibility for improving the system dynamic and steady-state responses as desired. While the final time constant decreases the transient response time and overshoot, the resulting undamped natural frequency leads to alleviation of steady-state error in the output voltage. The performance of the proposed control approach is evaluated via SIMULINK-based and real-time simulation results.