Synchronous reluctance motors (SynRMs) have attracted attention for various applications because they have no magnets and rotor windings. Thus, various methods for rotor position sensorless control of SynRMs at low speeds have been proposed. Similarly, we previously introduced a method for rotor position sensorless control of SynRMs at very low speeds. The proposed control method superimposes a high-frequency current with a small constant amplitude using a high-frequency current control system. The$q$-axis inductance of the SynRM considerably changes according to the load. In this paper, we show that the rotor position estimation error converges even under a large error between the predefined and real settings of the$q$-axis inductance of the SynRM model for position estimation when using the proposed method. Experimental results confirm that the proposed method achieves robust rotor position sensorless control against$q$-axis inductance variations even at very low speeds.