  For the strictly positive case (the suboptimal case), given stable rational
matrix functions $G$ and $K$, the set of all $H^\infty$ solutions $X$ to the
Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and
$\sup_{|z|\leq 1}\|X(z)\|\leq 1$, 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.
