Controlling weak grid-connected systems is very challenging. In transient, frequency and voltage oscillations may lead to voltage and/or frequency stability problems and finally lead to system collapse. During steady-state operation and at the point of common coupling, voltage degradation and grid voltage background harmonics restrict the inverter's functionality, reduce the power flow capability and cause poor power quality. With weak grid connection, grid impedance variance will contaminate the voltage waveform by harmonics and augment the resonance, destabilizing the inverter operation. In this paper, complete mathematical modeling is carried out and state feedback-plus-integral control is implemented to support the stabilization of the system. The proposed controller is adopted to provide a smooth transient under sudden load change by controlling the injected grid current under different grid inductance values. Furthermore, the proposed control is used to reduce the order and size of the inverter output filter while maintaining system stability. The proposed control has been compared with the conventional PI controller under different scenarios to validate its effectiveness and to strengthen its implementation as a simple controller for distributed generator applications.