§*H**¥**-*** Space: ***H**¥**-* is a
(closed) subspace of *L**¥* with
functions that are analytic and bounded in the open left-half plane. The *H**¥**-*
norm is defined as

§

•* **RH**¥**-* :
all proper real rational antistable transfer matrices.

•

• **Examples:** *H**2* functions: 1/s+1, e-hs/s+2, …

•* H**¥* functions: 5, 1/s+1, 5s+1/s+2, e-hs/s+2, 1/s+1+0.1e-hs,
…

• *L**¥* functions: 5, 1/s+1,1/(s+1)(s-2), 1/s-1+0.1e-hs, …