Single-phase inverters are widely used in different renewable energy applications. Although the full-bridge inverter istypically used, dual-buck inverters provide an important advantage, since they eliminate the shoot-through problems. However, solutions proposed in the literature require additional inductors, use linear controllersdesigned around an operation point, or cannot be used in grid-connected applications. This paper presents a hysteresis current control of a single-phase dual-buck full-bridge inverter for grid-connected active power injection. Includes the dynamical modelin state variables, as well as analytical conditions to guarantee the evolution of the error dynamics in a set with boundaries defined by the designer. Moreover, the paper provides guidelines for the design of the dead band required for the transitions between the positive and negative semi-cycles (and vice-versa) of the grid voltage. Finally, simulation results validate the main features of the controller as well as the design of the dead band