Compared to analog control, the adoption of digital control in LCL-type grid-connected inverters introduces control delays, which significantly alters the frequency characteristics of open-loop transfer functions of systems and imposes stricter stability requirements on the grid-connected inverter. Furthermore, in weak grid with wide-ranging variations in grid impedance, the robustness of the system is severely compromised. To bolster the resilience of the grid-connected inverter amidst fluctuations in grid impedance, this paper proposes a proportional-phase lag compensation strategy. By considering the control delays, stability analysis of the system is conducted within the bounds of grid impedance fluctuations, and stable regions are identified based on the Nyquist stability criterion, and then phase lag compensators and proportional parameters are properly designed. The resulting improved system adheres to the Nyquist stability criterion in weak grid, ensuring the grid-connected inverter to maintain stable operation, even amidst variations in grid impedance. Ultimately, the simulation outcomes confirm the viability and efficacy of the method proposed.