Optimality and dependence on g

There exists an admissible controller such that *||T**zw**||**¥*<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 *¥®*X**2 *, etc., and *K**sub** *®*K**2 *