This paper proposes a new control strategy for single-phase shunt active power filters (APFs) based on Lyapunov's stability theory. The idea in this strategy is to form an energy-like Lyapunov function in terms of the active filter states and then determine the control law that makes the time derivative of the Lyapunov function always negative for all values of the states. It is shown that a globally stable control is possible at the expense of a time-varying reference function for the direct current (dc) capacitor voltage. This method, however, requires the estimation or measurement of the harmonic ripple component on the dc capacitor voltage. Therefore, a modified control is proposed by ignoring this ripple component. The active filter's current reference is obtained by subtracting the measured load current from the generated supply current reference. The amplitude of the supply current reference can be adjusted by using a proportional-integral (PI) controller that regulates the dc capacitor voltage. Experimental results that are obtained for steady-state operation and step changes in the load are presented to verify the correct operation of the proposed control strategy.