The linear quadratic Gaussian Optimal control of a two-stage HFAC inverter system has been investigated in this paper. The uncertainty model of the high frequency resonant inverter is developed and analyzed with the input line and load variations taken into design considerations. The proposed control scheme has the advantages of fast response for both input line and load perturbations. It also ensures a wide range of system stability and guarantees robustness of the power converter. Both simulations and experimental results are provided to verify with the theoretical analysis through an experimental prototype with an output power of 500-W operating at 10 KHz and an output voltage of 24 V (peak value).