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Summary: With the rapid development of renewable energy, inverters have been widely used in the distributed power system. For the safety of the distributed power system, the stable operation of the inverter is vital. Hence, this paper detects slow‐scale instability fast‐scale instability and in the double‐loop proportional‐integral (PI) control single‐phase full H‐bridge inverter with inductive impedance load by the discrete‐mapping model firstly. Next, the mechanism of the mechanism slow‐scale and fast‐scale behaviors are explained by state‐space average model and Filippov method, respectively. Then, passive damping method and sine wave compensation techniques are extended to the system to suppress the nonlinear behaviors. Finally, the PLECS simulation and experiments are utilized to verify the correctness of the investigations. [ABSTRACT FROM AUTHOR]