Permanent Magnet Synchronous Machines (PMSMs) have several advantages, such as high ef¿ciency and low volume and weight, which make them attractive for aerospace applications and high performance servo drives. Matrix Converters (MCs) are an all-silicon alternative, with no bulky reactive elements, to the standard voltage source inverter. The most common control technique for such PMSM MC-fed drives is the so-called Field-Oriented Control (FOC), which requires the permanent magnet ¿ux position to achieve high dynamic performance. Encoders or resolvers are the most common sensing devices used for such a purpose, which not only increases the total cost of the PMSM drive but also adds extra electronics and cabling that may cause failures. This paper investigates and proposes an all range (from zero to full) speed hybrid sensorless FOC. The novelty of this paper relies on the use of a hybrid sensorless four quadrant FOC that averages the needed angle estimation from a model based angle estimator and a voltage pulse test injection angle estimator when feeding the PMSM with an MC instead of a standard voltage source inverter. Speed reversal and load impact simulation results are included, fully supporting the claims made in this paper Peer Reviewed