This article reviews six fundamental-wave excitation sensorless techniques for synchronous machines reported in the literature. All the techniques rely on a hybrid flux observer scheme, combining the voltage and current-models of the machine, and use the flux observer error signal to track the rotor phase angle and the rotational speed. A common mathematical framework with magnetic nonlinearity is constructed for the stability analysis where each of the studied technique is represented by a unique projection vector. The dynamics of the flux and the position observer is investigated and the regions of instability are identified for each scheme under similar operating conditions. Experimental validation to support the stability analysis is reported on a 1.1-kW synchronous reluctance machine test-bench.