Realizability of bilinear input/output difference equations: Corrections and extensions

This article studies the realizability property of discrete-time bilinear input-output (i/o) equations in the classical state-space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. Using new formulas for computing basis vectors of certain vector spaces of differential one-forms, we present in this paper the complete list of the third- and fourth-order realizable input-output bilinear models. Moreover, we provide a new realizable subclass of an arbitrary order.