qCorollary 12.3: Let g>0. G(s)=C(sI-A)-1B+D Î RH¥ and
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•
• where R=g2I-D*D. Then the following
conditions are equivalent:
• (i) ||G||¥ < g .
• (ii) ||D||< g and H has no eigenvalues on the
imaginary axis.
• (iii) ||D||< g and H Î dom(Ric).
• (iv) ||D||< g , H Î dom(Ric) and Ric(H)³0 (Ric(H)>0 if (C,A) is observable).
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