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:

(B.1)

Equation (3.46), applied to the first eigenvector, is written:

(B.2)

Developing the matrix relation, we obtain the following equation system:

(B.3)

The last two system equations are solved by the elimination of *p*_{31}, one of the two unknowns:

(B.4)

However , since μ_{1} ≠ 0 ∀ ω (cf. equation (3.34)). The only possible solution is ...

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