%0 Journal Article
%T State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
%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) the maximum entropy solution $X$ to the Leech problem $G(z)X(z)=K(z)$ and $\|X\|_\infty=\sup_{|z|\leq 1}\|X(z)\|\leq 1$, with $G$ and $K$ stable rational matrix functions, is proved to be a stable rational matrix function. An explicit state space realization for $X$ is given, and $\|X\|_\infty$ turns out to be strictly less than one. The matrices involved in this realization are computed from the matrices appearing in a state space realization of the data functions $G$ and $K$. A formula for the entropy of $X$ is also given.
%U http://arxiv.org/abs/1408.2144v1