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This paper proposes a robust controller combined with extension theory (ET) and applies it to the speed control of a brushless DC motor (BLDCM) drive system. The controller uses the motor’s speed error and its rate of change as characteristic values to establish ET classical domain and neighborhood domain models. Appropriate weights are set, and then the real-time speed error and its rate of change are used as input to calculate their correlation function with the ET model. The system can automatically determine the optimal proportional–integral (P-I) parameters, enabling the controller to perform real-time adaptive adjustments in response to the system’s nonlinear and time-varying characteristics. This overcomes the shortcomings of traditional fixed-gain P-I controllers with insufficient response during speed tracking and load changes. Furthermore, the system is equipped with a synchronous reference frame-based sliding mode observer (SRF-SMO) to achieve speed sensorless control. A power factor correction (PFC) circuit and over-voltage and over-current protection circuits are added to the drive system to improve the power quality at the power source and the operational safety of the drive system. To verify the effectiveness of the proposed controller, this paper implements the control algorithm on a 32-bit floating-point digital signal processor (DSP) TMS320F28335 using PSIM SimCoder’s automatic code generation technology. The experimental results show that compared to three different sliding mode controllers (SMCs) designed with constant speed reaching law (CSRL), exponential reaching law (ERL), and extension theory combined with exponential reaching law (ETERL), the proposed extension theory robust speed controller exhibits superior control performance in speed command tracking and load regulation response. This demonstrates that the proposed robust controller not only possesses stronger anti-disturbance capability, smaller speed drop, and shorter recovery time but additionally, the power factor of the drive system under rated load can reach above 0.98, and the protection mechanism can be activated under both over-voltage and over-current conditions, allowing the drive system to operate safely. Full article