This article proposes a robust inertial controller for converter-based distributed generators employed in low-inertia power systems like microgrids. The increasing penetration level of renewable energy sources based on power electronics converters in modern power systems reduces the inertial features of the system. It also increases concerns associated with the system uncertainty and sensitivity against disturbances. To cope with these challenges, by employing the proposed linear matrix inequality (LMI)-based mixed H 2 / H ∞ robust method, an optimal robust controller aided for inertial support as well as fast frequency restoration is provided. Using the proposed solution not only presents a better inertial response but also proposes a faster frequency restoration, by which the system’s frequency can be restored immediately following any disturbance, even in the presence of system uncertainties. Through in-detailed frequency response analysis and time-domain simulations for different scenarios, it is illustrated that the proposed mechanism can be successfully employed to address the inertial requirements in power electronic-based power systems. In addition, the proposed LMI-based mixed H 2 / H ∞ control solution is compared with a number of other solutions to illustrate its better performance against disturbances. Simulation results validate the merits and effectiveness of the proposed controller.