In works [1-4] the multiprogram stabilization problem (MPS problem) is considered for various classes of continuous control systems. Such systems are described by ordinary differential equations. In the article [5] for the first time this problem has been solved for a linear model of a digital object, i.e. for the linear difference system. Here we consider the bilinear control systems. This is broader class that allows simulating processes in various applications [6-9]. So it is important to extend multiprogram approach to the class of bilinear discrete control systems.