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Condition(3.6)followsfrom (3.8~)and (3.10). Condition(3.5)then followsfrom (2.4) and (3.2). v v v
 

Summary: Condition(3.6)followsfrom (3.8~)and (3.10). Condition(3.5)then
followsfrom (2.4) and (3.2). v v v
The followingcorollarydemonstratesthat for y = 1, the internally
balanced structure minimizes J in (3.4) while for y = SIN the optimal
low noise structures[11, [2] minimizeJ. Both these structures are optimal
for y = 1and S = N.
Corollary:
i) y = 1implies KT = W,in (3.5). For U = V = Zin (3.2a), the
optimal T = X-'/*whichimplies
K T = W T = C . (3.11)
ii) For y = S/Nand U = I, the optimal T = (S/N)'j*C-'/2V'which
implies
in which case
tr [ W,] =-
S*
N
(3.13)
Furthermore, there exists a transformation T such that in addition
(KT),j=1for all j . (3.14)
iii) If S = N, then both the internally balanced structure(3.11) and the

  

Source: Antsaklis, Panos - Department of Electrical Engineering, University of Notre Dame

 

Collections: Engineering