L¥ and H¥ Spaces
§L¥ (jR) Space: L¥ (jR) or simply L¥ is a Banach space of matrix-valued (or scalar-valued) functions
that are (essentially) bounded on jR, with norm
RL¥ (jR) or simply RL¥: all proper and real
rational transfer matrices with no poles on the imaginary axis.
§H¥ Space: H¥ is a (closed) subspace of L¥ with functions that are analytic and bounded in the open
right-half plane. The H¥ norm is defined as
The
second equality can be regarded as a generalization of the maximum modulus theorem for matrix
functions. See Boyd and Desoer [1985] for a proof.
RH¥: all proper and real
rational stable transfer matrices.
