Abstract: Due to the influence of grid impedance,the photovoltaic（PV）grid-connected inverter may be unstable under the weak grid.This paper proposes a digital H_∞ robust controller design method for PV grid-connected inverter. Firstly,this work establishes the control model of PV grid-connected inverter under the traditional control strategy,and analyzes its stability under weak grid. In order to improve the robustness of LCL-filtered PV grid-connected inverter against the variation of grid impedance,the standard H_∞ control model of PV grid-connected inverter is established in discrete domain with considering the influence of digital control delay. And the digital H_∞ controller is designed by appropriately selecting the weighting functions. Compared with the traditional dual current loop control strategy,the simulation and experimental results in this paper prove that the designed digital H_∞ controller significantly enhances the stability of PV grid-connected inverter in weak grid.