On minimal realizations of first-degree 3D systems with separable denominators

In this paper, we focus on first-degree three-dimensional (3D) causal systems which have separable denominators. Gröbner basis is applied to prove that not all first-degree 3D systems with separable denominators have minimal realizations (of order 3). This is in contrast to 2D systems with separable denominators which always admit absolutely minimal realizations. Two illustrative examples are presented.