Abstract: The accurate and rapid estimation of rotor position and speed is a critical challenge associated with the sensorless control of high-speed permanent magnet synchronous motors (PMSMs) employed in hydrogen fuel-cell air pumps. These applications demand high efficiency, reliability, and dynamic response, making the limitations of conventional position sensors, such as increased cost, increased size, and reduced robustness, particularly prohibitive. However, obtaining precise rotor information within an extremely short period using sensorless algorithms remains a significant challenge, especially under high-speed operating conditions where system nonlinearities and parameter variations become more pronounced. This paper introduces a novel observer design termed the predefined time-space super-twisting sliding mode observer (PdT-ST-SMO). The core innovation of the proposed scheme lies in a spatial division strategy that partitions the system state space into two distinct operational regions: the barrier-function region and the rapid-reaching region. When the system state is in the rapid-reaching region, a newly designed, predefined time–space reaching law is activated. This law ensures that the observation error converges toward the sliding manifold with maximum expediency, minimizing the initial reaching phase and setting a user-defined upper bound on the convergence time, independent of initial conditions. Once the system state enters the vicinity of the sliding surface (the barrier-function region), an improved barrier function is employed. This function dynamically adjusts the observer gain, ensuring that the system trajectory remains within a predefined boundary layer around the sliding surface. The barrier function suppresses high-frequency oscillations known as chattering—a persistent issue associated with conventional sliding-mode control that can degrade control performance and cause mechanical wear or acoustic noise. The proposed observer is fundamentally constructed upon the super-twisting sliding mode algorithm. By integrating the predefined time–space reaching law and improved barrier function with the super-twisting algorithm, the observer achieves a superior balance among rapid convergence, high steady-state accuracy, and effective chattering mitigation. To validate the stability and convergence properties of the PdT-ST-SMO, the Lyapunov stability theory is applied. This theoretical analysis demonstrates that the current observation error of the designed observer converges to a predefined neighborhood of the origin within a predefined time. Comprehensive simulation studies are conducted to verify the performance of the proposed approach. For a target speed of 1000 r·min⁻¹, the proposed observer can achieve the convergence of the rotor position observation error within a predefined time T. For comparative analysis, the proposed observer is benchmarked against a traditional sliding-mode observer (SMO) and a conventional super-twisting SMO (ST-SMO) under identical operating conditions; the results show that the accuracy of the proposed observer improved by 73.33% and 70.91%, respectively, relative to the two established observers. This enhancement in observation accuracy, coupled with the predefined-time convergence and effective chattering suppression, underscores the superiority of the proposed PdT-ST-SMO design. The scheme effectively addresses the sensorless control challenge for high-speed PMSMs in hydrogen fuel-cell air pumps, laying a solid foundation for enhancing the overall efficiency, dynamic response, and operational stability of hydrogen fuel-cell systems.