The aim of this paper is to present the mathematical proof of convergence of a position sensorless control algorithm. This algorithm is applied to control a drive with a nonsalient pole permanent magnet synchronous machine in low speed range including standstill. This paper shows that the convergence of this sensorless method does not depend on the machine parameters providing good robustness with respect to parameter uncertainties. In addition, the minimum saliency required for sensorless operation at zero speed is determined. The effectiveness of this technique is verified by simulation and experimentation on an eight-pole 1 hp-1000 r/min test machine. The experimental results confirm the effectiveness of the sensorless algorithm and the validity of the theoretical analysis.