The idea of extending the comprehensive theory of state space realization for linear systems to certain classes of nonlinear systems has been the subject of much recent research in mathematical system theory. One such class are those systems with a bilinear input/output map, first considered by Kalman [Pattern recognition properties of multi-linear machines, IFAC Symposium on Technical and Biological Problems of Control, Yerevan, Armenian SSR, September, 1968] in 1968. Kalman’s paper raised many questions concerning the canonical realization of such an input/output map; in particular it demonstrated that the proposed realization procedure could lead to a nonreachable realization. More recently, Sontag and Rouchaleau [On discrete-time polynomial systems, J. Non-linear Analysis, Theory, Methods, and Appli-cations, 1 (1976), no. 1, pp. 55–64] have shown that the required concept to be applied in this case is “quasi-reachability,” i.e. that the state set of the realization is the closure (in the Zariski topol...