This paper proposes a novel approach for calculating position-dependent inductance matrix of slotted permanent magnet synchronous motors (PMSMs) and advanced analytical models for machine voltage and torque. In a real PM machine, the slotted structure of the stator and rotor causes unintended variations in air-gap permeance and magneto-motive force (MMF). The proposed approach analyzes the effects of these variations on air-gap flux and winding inductances. The calculated d-q inductance matrix contains harmonic and coupling components. In this paper, both voltage and torque models are modified to reflect the changes in inductance matrix. Some nonlinear terms due to structural saliency are additionally considered. The results of simulation with finite-element method (FEM) are presented to verify the validity of the proposed inductance, voltage and torque models.