CHECKING THE VALIDITY OF D, G SCALING MATRICES

Consider Дб? scaling matrices, which satisfy at frequency wo:

( DM {jwo)D~l

 

– )G F-1/4) < 1

 

(10.27)

 

p

 

and:

Let then:

Let tjm the real negative eigenvalue of % of maximal magnitude. Then: 1 uj = u)q H– Vm

(10.34)

Let then r}p the real positive eigenvalue of mi of maximal magnitude. Then:

_ 1

u> = loq H

Op

Proof:

• Note as a preliminary that (see equation (10.31)):

and:

Fi(H(uo), 6ulm) = Hu + 6uHl2{Im ~ 6ljH22)-1H21 (10.36)

As a consequence:

F~1/4 1 _ f_1/4 = Ріфл6шІт) [10]