For the strictly positive case (the suboptimal case), given stable rational
matrix functions G and K, the set of all Hβ solutions X to the
Leech problem associated with G and K, that is, G(z)X(z)=K(z) and
supβ£zβ£β€1ββ₯X(z)β₯β€1, is presented as the range of a linear
fractional representation of which the coefficients are presented in state
space form. The matrices involved in the realizations are computed from state
space realizations of the data functions G and K. On the one hand the
results are based on the commutant lifting theorem and on the other hand on
stabilizing solutions of algebraic Riccati equations related to spectral
factorizations.Comment: 28 page