In this study, an extended Lyapunov-function-based control strategy that assures global asymptotic stability is proposed for single-phase UPS inverters. The Lyapunov function is formed from the energy stored in the inductor and capacitor due to the fact that the system states converge to the equilibrium point if the total energy is continuously dissipated. It is shown analytically that the classical Lyapunov-function-based control leads to a globally asymptotically stable system at the expense of steady-state errors in the output voltage, which exist due to the lack of outer voltage loop in the control input. Therefore, an extended Lyapunov-function-based control strategy is proposed, which eliminates the steady-state error without destroying the global stability of the closed-loop system. The steady state and dynamic performance of the proposed control strategy has been tested by simulations and experiments under resistive and diode bridge rectifier loads. The results obtained from a 1-kW inverter demonstrate that the developed control strategy not only offers global stability, but also leads to good quality sinusoidal voltage with a reasonably low THD, almost zero steady-state error in the output voltage, and fast dynamic response under linear and nonlinear loads.