The buck-boost DC-AC inverter generates an alternating output voltage as the differential voltage of two DC-DC individual buck-boost converters that are driven with two 180° phase-shifted DC-biased sinusoidal references. The peak value of the inverter alternating output voltage does not depend on the direct input voltage. In addition, an advantage over the Boost DC-AC inverter is that the output voltages of both Buck-Boost converters are also independent of the direct input voltage. The difficulty of the topology lies in the control of both buck-boost DC-DC converters as they are required to work with variable operating-points. A double-loop control strategy is proposed for the buck-boost DC-DC converter with a new inner control loop for the inductor current and also a new outer control loop for the output voltage. These control schemes include different compensations that make possible a fast and accurate control of both converters with variable operating points. With these compensations, the controllers are easy to design, implement and develop. Furthermore, feedforward loops are included to increase the robustness of the inverter to external disturbances in both the input voltage and output load. The proposed control strategy is designed and implemented on a prototype 1.5 kW buck-boost DC-AC inverter. The control strategy is validated by means of both simulation and experimental tests. The results show that the proposed strategy achieves a robust, reliable and accurate control of the inverter even in hard situations such as nonlinear loads, sudden load changes and transient short circuits.