§Characterization: Let g > 0   and                                  Then
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• where
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• and  R =g 2I-D*D.
§Proof: Let F(s) =g 2I-G~(s)G(s).
§ Then ||G||¥ < g  Û   F(jw)>0, " wÎ R È {¥}Û detF(jw)¹ 0, " wÎ R since F(¥)=R>0 and F(jw) is continuous. Û   F(s) has no imaginary axis zero. Û   F -1(s) has no imaginary axis pole.
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• Û   H has no jw axis eigenvalues if the above realization has neither uncontrollable modes nor unobservable modes on the imaginary axis.