# CHECKING A POSTERIORI THE VALIDITY OF D, G SCALING MATRICES ON A FREQUENCY INTERVAL

A technical Lemma, which is the basis of this section and coincides with Lemma 2..4 of chapter 8, is presented in the first subsection. The second subsection proposes a method for introducing the frequency ш as an additional uncertainty (see section 3. of chapter 7 for alternative methods). The technique for checking the validity of D, G scaling matrices on a frequency interval is finally presented in the third subsection.

3.3 A TECHNICAL RESULT

Let Fi(M, A2) the LFT transfer between w and z in Figure 10.1. Д2 is a real diagonal model perturbation, whereas the complex matrix M is partitioned as:

The transfer between w and z is thus:

Fi(M, Д2) = Mu + Mi2A2{I — М22Д2)_1М2і LEMMA 4..1 Let:

Assume that а(Мц) < 1 and let к < 1//^д2(М22)- Then:

a(Fi{M, Д2)) < 1 УД2 Є кВА2 (10.17)

if and only if:

det(I – AG) ф 0 УД2 Є kBA2 (10.18)

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