Let $G(z)$ denote the (rational not necessarily square and unstable) transfer function of an nD system, where $z=(z_{2},...,z_{n})$, of a discrete spatial-temporal recurrence Givone-Roesser type system or Fornasini-Marchesini type system.
I need to solve the following problem:
Find rational stable (or structurally stable) scalar function $g(z)$ such that $g(z)G(z)$ is stable (or structurally stable) such that $\left||g(z)-1\right||_{\infty}$ is minimal among all $g(z)$ as above.
Can the problem be solved directly, without the use of Schur-Agler type interpolation and without using LMI methods (finite or infinite)?
By $P(z)=g(z)G(z)$ stable, we mean that for each entry $P_{i,j}(z)=n_{i,j}(z)/d_{i,j}(z)$ the denominator $d_{i,j}(z)$ has no zeros in the unit open polydisc ${\mathbb D}^{n}$, and by structuraly stable, we mean that $d_{i,j}(z)$ has no zeros in the unit close polydisc $\overline{\mathbb D}^{n}$, where in any case we assume that $n_{i,j}(z),d_{i,j}(z)$ are relatively prime.
Many Thanks!
