Large-scale photovoltaic (PV) plants may be destabilised by the large grid impedance introduced by transformers and long transmission lines. When considering the digital control delay of grid-connected inverters, the problem will become more serious. In this study, the equivalent impedance model of digitally controlled large-scale PV plants is established, considering that the values of the parameters of the LCL filter follow Gaussian distributions. Then, the system stability can be analysed conveniently, and the stability analysis shows that the digital control delay will make the system robust to large grid impedance worse. To enhance the stability-robustness of the system, an H ∞ robust controller is proposed in this study. By properly selecting the weighting functions, the desired tracking error performance and robustness are achieved on the basis of the mixedsensitivity optimisation control design. Compared with the traditional dual current loop control strategy, the H ∞ robust controller improves significantly the system stability-robustness against large grid impedance. Finally, simulation and experimental tests are carried out in this study, and the results demonstrate the effectiveness of the proposed H ∞ robust controller.