Conventional inverter upper and lower tubes cannot conduct simultaneously and dead time leads to current distortion, a strategy based on improved repetitive control under Z-source grid-connected inverter is proposed. It reduces the harmonic content of output voltage and upgrades voltage waveform. The mathematical model of Z-source grid-connected inverter is constructed, and with the state space of standard controller, Lyapunov theory is used to derive the design conditions of the state feedback control law based on the linear matrix inequality; then numerical solutions are carried out to obtain the parameters of the controller to ensure the system’s robustness, and finally the feasibility is verified by simulink simulation.