State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution

Abstract

For the strictly positive case (the suboptimal case) the maximum entropy solution $X$ to the Leech problem $G(z)X(z)=K(z)$ and $\Vert X{\Vert }_{\infty }={\sup }_{|z|\le 1}\Vert X(z)\Vert \le 1$, 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 $\Vert X{\Vert }_{\infty }$ 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.

19 pages

References in corpus (1)

• State space formulas for stable rational matrix solutions of a Leech problem