Since *W*(*s*) has no *j**w*-axis zeros, we conclude that ||*G*||¥ < *g** .*

(vi) Û (vii): follows
from Schur complement.

(vi) Þ (i): by following
the similar procedure as above.

(i) Þ (vi): let

Then
there exists an e>0 such that ||*G*e||¥ < *g** .* Now (vi) follows by applying part (v) to *G*e *.*