The achievement of step-up inversion with a boost DC/AC converter requires appropriate periodic references for inductor currents, which have to satisfy ordinary differential equations (ODE) of the Abel type. These are equations with highly unstable solutions for which the existence of periodic solutions remains unproved. Hence, the studies reported so far in this subject obtain periodic output voltages that approximately track the expected profile using different periodic current references that do not exactly satisfy the Abel ODE. However, neither an explanation of why are periodic output voltages still obtained, nor an assessment of the output voltage error is provided. This paper analyzes the effect of using periodic current references in a Lyapunov-based controlled boost DC/AC converter performing step-up inversion tasks. It is shown that, for sufficiently accurate current references, the system exhibits asymptotically stable periodic solutions with bounded error. Moreover, the paper propounds the use of Harmonic Balance (HB)-based techniques to obtain such current references. Simulation and experimental results confirm that this choice yields periodic output voltages with an error that may be lowered using higher HB approximations.