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The focus of this paper is on the notion of an extended observer based on Input-output feedback linearization control. The mean value theorem (MVT) and sector non-linearity approaches were implemented for a class of the Lipchitz model of Permanent Magnet Synchronous Machine (PMSM). Based on these mathematical approaches, the proposed design allows the expression of nonlinear error dynamics for the extended observer become a convex combination of known matrices that have time varying coefficients. This is similar to a linear parameter varying (LPV) systems after the non-linear system of the PMSM is represented in the Lipchitz form. Through the Lyapunov theory, one can obtain and express the stability conditions in a term of linear matrix inequalities (LMI). The extended observer gain is separately determined based on the separation principles by the exploitation of YALMIP software. Furthermore, this gain have complete independence from the PMSM states. As a proof of the efficacy of the proposed approach, one applies an illustrative simulation to the sensorless Field Oriented Control (FOC) of the PMSM drive by utilising the MATLAB/SIMULINK environment.

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