I. Introduction
Bilinear forms were addressed in the literature in different ways and contexts [1] –[16]. Most often, they are related to the approximation of nonlinear systems. In other words, a bilinear model can approximate a large class of nonlinear systems via a finite sum of the Volterra series expansion between the inputs and outputs of the system. In this context, the bilinear systems behave similarly (to some extent) to linear models, which further simplify the analysis. Due to this simplicity, they were involved in a wide range of applications, e.g., digital filter synthesis [5], prediction problems [6], channel equalization [7], echo cancellation [8], chaotic communications [12], active noise control [13], [15], neural networks [16], etc. Nevertheless, in all these frameworks, the bilinear term is defined with respect to the data, i.e., in terms of an input–output relation.