On applicability of LPV tools for bilinear systems

In linear parameter varying (LPV) systems, the relations between signals are considered to be linear, but the model parameters are assumed to be functions of time-varying signals. It has been claimed in the literature that as a result of this parameter variation, the class of LPV systems may describe both time-varying and nonlinear phenomena. The goal of this paper is to study at what extent the tools worked out for realizability of LPV systems are applicable for nonlinear control systems. For that purpose the realizability of the 2nd order discrete-time bilinear control systems is studied.