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The control of a grid-connected voltage source inverter with an inductive-capacitive-inductive (LCL) filter is a very challenging task, since the LCL network causes a resonance phenomenon near to the control stability boundary. While many active damping methods have been proposed to overcome this issue, the role that pulse width modulation transport delay plays in the effectiveness of these strategies is still not fully resolved. This paper presents a theoretical discrete time-analysis framework that identifies three distinct regions of LCL filter resonance, namely, a high resonant frequency region where active damping is not required, a critical resonant frequency where a controller cannot stabilize the system, and a low resonant frequency region where active damping is essential. Suitable controllers are then proposed for the two stable regions, with gain calculations that allow for the greatest system bandwidth and damping. Simulation and experimental results verify the presented analysis.