In the permanent-magnet synchronous machine (PMSM) drive system, the adoption of silicon carbide (SiC) devices brings up new challenges, such as overvoltage, electromagnetic interference emission, and bearing current. To surmount these barriers, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filter designed as the sine wave filter can be introduced into the machine drive system. However, filter and stator inductance can create unwanted electrical resonance issues. For the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -equipped PMSM drive system, there are two main factors that cause the drift of resonant frequency and change of stable region: (1) synchronous coordinate transformation with variable fundamental frequency, (2) parameter variations due to the magnetic saturation effect. In this paper, the deviation of resonant frequency caused by coordinate transformation is discussed. Then, the inherent damping effects and stability range in the rotating reference frame are derived in detail. Furthermore, considering the parameter mismatch disturbances, an active damping method based on the enhanced notch filter is presented, of which notch frequency is designed lag behind the nominal resonant frequency. The accurate discretization method and theoretical stability analysis in discrete <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> -domain are conducted. The experimental results are presented to verify the effectiveness and robustness of the proposed analysis and method.