Abstract: Based on the working principle of the three-phase four-leg inverter, the mathematical model of control systems is established by switching functions. The discrete system is then transformed into a continuous system by the average switch period operator. Further, the state variables, input variables and output variables are selected according to the main control objectives of the system and later three-input three-output affine nonlinear system models compatible with differential geometry methods are obtained. The resulting model is proved in the nonlinear differential geometry theory to meet conditions for the exact linearization of MIMO (multi-inputs and multi-outputs) systems and the nonlinear state feedback control laws are also deduced. For the resulting linear system after nonlinear coordinate transformation, a closed-loop system energy function is proposed by the idea of passivity control, when the quadratic optimal control strategy is adopted. Finally, the weight matrix in parametric form is deduced and the optimal control law of the original system is recovered by inverse transformation from the optimal control of linear systems. Simulation results demonstrate the effectiveness and correctness of the proposed control method.