Partial realization of symmetric matrix rational functions (Q1103027)

In matrix terms the partial realization problem of classical systems theory is: given a finite list of constant matrices \(G_ i\) \((i=1,...,s)\) find matrices A, B, C with A of smallest possible dimension such that \(G_ i=CA^{i-1}B\) for each i. The present paper is based on earlier work of the author [ibid. 73, 171-196 (1986; Zbl 0589.15017) and Int. J. Control 43, 1177-1199 (1986; Zbl 0589.15018)]. It describes a method of solving the partial realization problem in the case where the \(G_ i\) are symmetric. The method does not work in all cases, nor does it solve the problem completely, but it does give a complete solution in the ``generic'' case.