This paper proposes a proportional multiple-integral (PMI) observer-based state feedback fault-tolerant controller design method for stabilizing distributed electric propulsion aircraft in the event of actuator failures. In this method, an augmented error system is constructed where the \( n \) -th derivative of the fault signal is reconstructed as part of the external disturbance to the system. The PMI observer is designed based on the robust \({H_\infty }\) control theory, which can estimate both unmeasurable states and faults. A constrained multi-objective algorithm formulated with linear matrix inequalities (LMIs) is used to effectively mitigate the impact of external disturbances on the system. Subsequently, a state feedback fault-tolerant controller is designed based on real-time estimation information of the aircraft’s state and faults, ensuring that the aircraft remains stable even in the presence of faults. The stability of the closed-loop system are proven using Lyapunov theory. Finally, simulation experiments validate the accuracy and rapidity of the fault estimation algorithm and the stability of the aircraft under various fault modes.