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In this paper, the stability analysis of a grid-connected voltage source inverter with an LCL filter is presented. The Poincaré map is used to analyze the stability of the system from a geometric point of view and provides a better understanding of the system performance. In addition, a composite nonlinear feedback (CNF) control is proposed in order to improve the transient and steady-state performance of the control system. Simulation and experimental analysis verify the validity of the analysis and also show the superiority of the CNF-based controller compared to the conventional proportional-resonant controller during transients and steady-state operation.