There exists an admissible controller such that ||Tzw||¥<g iff the following three conditions
hold:
(i) $ a stabilizing X¥ >0
(ii) $ a
stabilizing Y¥ >0
(iii) r(X¥Y¥)<g2
• Denote by g0 the infimum over all g such that (i)-(iii) are satisfied. Descriptor formulae can be
obtained for g =
g0
• As g ®¥, H¥ ®H 2 , X ¥®X2 , etc., and Ksub ®K2