The nonlinearities of the load current in power systems are increasing with the growing number of electronic devices with rectifiers at the front end of their power supply. Therefore designing an inverter that can overcome these nonlinearities in the output current and generate an AC output voltage within the desired Total Harmonic Distortion (THD) level is critical to meeting the power quality requirements defined by international standards. In this paper, a backstepping controller combined with two novel current observers is proposed for the control of a single-phase H-Bridge inverter. A Lyapunov stability analysis is utilized to demonstrate system stability. Simulation results validate the performance of the control scheme in the presence of both linear and nonlinear loads in terms of meeting the tracking objective as well as the THD requirements of IEEE 519 and EN 50160.