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.