Abstract This paper presents a robust control scheme for power electronic interfaces of grid-tied fuel cell power plant. Firstly, a linear matrix inequality (LMI)-based PID controller is designed to control the duty cycle of the boost DC/DC converter, aiming to adjust the output DC voltage to an arbitrary reference value. Afterwards, linear parameter-varying (LPV) technique is utilized for robust control of grid-connected inverter to follow the desired real and reactive power demand of the grid, considering time-varying load and uncertain grid-impedance. Taking uncertainty of the system into account, all admissible variations are considered as a convex polytope. To guarantee a prescribed disturbance attenuation level and improve the transient response of the closed-loop system, H∞ approach is exploited with pole placement consideration in terms of LMIs. Simulation results of the proposed controller compared to those of conventional PI controller, in presence of grid-voltage disturbance, validate high efficiency of the designed control.