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This paper describes a control method for single-phase transformerless grid-connected inverter system for photovoltaic (PV) application. The system consists of a DC-DC Boost Converter and a full-bridge inverter. The DC-DC Boost Converter implements a Sensorless Maximum Power Point Tracker (MPPT) algorithm with regulated DC bus voltage while the full-bridge inverter implements a Hysteresis Current Control as the control method. These control method provides robust current regulation, achieve unity power factor, low THD and optimize the PV energy extraction suitable for grid connected PV systems. Simulation and experimental results are provided to demonstrate the effectiveness of the design.