In this paper, the AC-DC interface system is studied to realize energy mutual aid in hybrid microgrid. Considering the uncertainties and fragilities of the system, the non-fragile robust H-infinity control is adopted to stabilize the AC-DC bus voltages. At the same time, taking the dynamic response characteristics into account, combined with the Linear Matrix Inequalities (LMI) regional pole placement method, and the non-fragile robust stability controller is proposed for the AC-DC interface system. Simulation results show that the designed controller has better control performances with respect to uncertain parameters, external disturbances and controller gain perturbations, which satisfy the requirements of stability, robustness and high precision control of AC-DC interface system in hybrid microgrid. This work is supported by National Natural Science Foundation of China (No. 51777027) and Key Research and Development of Technology Plan of Jilin Province (No. 20180201010GX).