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. INTRODUCTION OF THE FREQUENCY
Figwe 10.2. Introduction of frequency as a parametric uncertainty.
In order to apply the previous Lemma, an LFT model is to be derived for the dynamic system M(s), in which the frequency appears as a real parameter. The issue is more precisely to determine a complex matrix H such that, for a given strictly positive frequency uiq:
M(j(uj0 + 6u>)) = Fi(H(loq), Swim) V6u> > – loq (10.19)
Let (A, B,C, D) a state-space representation of M (s), and m the dimension of matrix A. It is well known that (see Figure 10.2 with s = j(uiQ + 6ш)):
/6u>-ui0, M(j(uJo + Sui)) = F,(Mo, 7™ ) (Ю.20)
V шо + дш/
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with:
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Further note that:
with:
T= — ( Ir? Ijp )
CUq V lm *m)
As a consequence:
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