To be able to calculate the transfer matrix in the case of an interior permanent magnet synchronous motor (IPM-SM), we will initially calculate the eigenvectors associated with the eigenvalues of the evolution matrix.
The four row eigenvectors , , and , constitute the 4 × 4 transfer matrix:
Equation (3.46), applied to the first eigenvector, is written:
Developing the matrix relation, we obtain the following equation system:
The last two system equations are solved by the elimination of p31, one of the two unknowns:
However , since μ1 ≠ 0 ∀ ω (cf. equation (3.34)). The only possible solution is ...