%0 Journal Article
%T State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
%A A. E. Frazho
%A S. ter Horst
%A M. A. Kaashoek
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1408.2145v1