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Taking aeronautic static inverter as the research object, the Z-source inverter is introduced to design aeronautic static inverter For its traditional two-stage structure with low efficiency and complex system and the waveform distortion caused by the dead zone effect. This paper introduces a feedback control strategy based on a high-order differentiator for the problem of complex controller design due to the high order and non-minimum phase of Z-source inverter system. The controller uses higher-order differentiators to estimate the system state variables at each order and does not depend on an exact system model. Simulation experiments show that this feedback controller can effectively track the given output voltage when used for Z-source inverter output voltage control, and maintain good steady-state and dynamic performance when the system is subject to external disturbances, meeting the aeronautic static inverter control requirements