Z-source inverter takes advantage of a distinctive impedance source network and modulation method of shootthrough vector, and achieves the function of buck/boost DC -AC inverter in the single stage system at the same time, which is suitable for grid-connected PV systems with large input voltage variations. The purpose of this study is to draw a unified method of shoot-through vector and grid inverter of the z-source inverter, apply the method of state-space averaging for the modeling analysis of the z-source inverter and give a complete mathematical model. Based on which and according to the nonlinear control theory and making use of the linearization of affine nonlinear model of the z-source inverter, we can get the specific derivation of equation. The results of the simulation and experiment show that according to the linearization of the shoot-through vector with affine nonlinear model for the z-source, we can make the system have the characteristics of fast and accurate tracking, small overshoot, small DC voltage, AC current ripple and small THD, and it has a certain practical value.