. A PRELIMINARY TECHNICAL RESULT

. A PRELIMINARY TECHNICAL RESULT

A technical Lemma is needed, which forms the basis of the Main Loop Theorem (see subsection 4.4 of chapter 1). Let P a complex matrix and Ді and Д2 two mixed model perturbations. The two interconnection structures of Figure 12.4 are equivalent, if Д = diag( Ді, Д2). Partition then compatibly P as:

LEMMA 3..1 If matrices I — P22A2 and I — РцДі are invertible, then:

det(I-PA) = det{I-P22A2)det{I-Fi{P, A2)Ax)

= det{I – PnAi)det{I – Fu{P, Ax)A2) (12.11)

Proof: A classical property of the determinant is used:

Подпись: det where D is invertible. {c d) = det(D)det(A ~ BD~lC) (12.12)

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