Sampling and computational delay are necessary in digital control, though they may alter the characteristics of the actual controlled plant when considered in the discrete domain. Accordingly, this article establishes a mathematical model of a single-phase grid-connected inverter with an LCL filter in the discrete domain. Three active damping control delay times: 0, [GRAPHICS] , [GRAPHICS] are analysed, considering the influences introduced by digital control of the plant. Further, the range of the capacitor current feedback coefficient used in active damping control is derived to guarantee that the controlled plant does not have poles outside the unit circle. Using Nyquist diagrams, the proper proportional-resonant (PR) controller parameters can be intuitively determined. The theoretical analysis is verified using MATLAB and a 3kW laboratory prototype based on a digital signal processor (TMS320F2808).