Coprimeness properties of nonlinear fractional system realizations

In this paper, the relationship between the Bezout and the set-theoretic approaches to left coprimeness is studied. It is shown that left coprimeness in the set-theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relations between two left coprime realizations of the same system.