This article presents the mathematical model of a 2 KW DBI (Dual Buck Inverter) converter that can be used in renewable energy applications. The inverter operating modes are described with the equations that model their behavior with the activation signals of the MOSFETs. The switching model is built. Simulation results are presented by applying linear control through a PI controller and GPC (Generalized Predictive Controller) hybridized in PID structure; simulation results are recorded in PSIM© verifying the control response due to changes in the load and the input DC voltage level.