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In this paper, we proposed a robust controller for high frequency resonant inverter. High frequency resonant inverter requires fast dynamic response and tight control of the output voltage. The component tolerance, load and line variation as well as small signal model inaccuracy all impose challenge in the controller design, while as such inverter feed open AC bus with dynamic load change, robust stability and robust performance become even important. We used the H∞ robust controller synthesis method to design a 3-order controller for the an APWM resonant inverter. Firstly uncertainty model of the inverter system was derived. A standard robust control problem was set-up and optimal controller was obtained and reduced to a 3-order controller, taking advantage of the Matlab robust toolbox. Simulation results for the closed-loop system under various perturbations verified the advantages of the proposed controller.