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This paper proposes a speed synchronization strategy for single-inverter dual-parallel (SIDP) permanent magnet synchronous motor (PMSM) drives using the damped least squares (DLS) method. Within the master-slave motor structure, where only the master motor is directly regulated for speed and current, the proposed method synchronizes the slave motor speed to that of the master motor by generating the master motor d-axis current. The d-axis current is generated as a nonlinear function of the rotor angle difference between the two motors. This function contains a mathematical singularity at zero rotor angle difference, where it becomes undefined or diverges to infinity. If not properly compensated, this singularity may cause numerical instability and abrupt current variations. The proposed method employs damped least squares (DLS) to suppress instability at zero rotor angle difference and to maintain smooth current flow, thereby ensuring stable synchronization of the two motors under diverse load conditions. The effectiveness of the method is validated through both simulation and experimental results.