On Uncontrollable Discrete-Time Bilinear Systems Which are “Nearly” Controllable

In this note, for a class of uncontrollable discrete-time bilinear systems, it is shown that the controllable region “nearly” covers the whole space while the uncontrollable region is only a hypersurface. As a result, for almost any initial state and any terminal state of the system, the former can be transferred to the latter. In addition, the two-dimensional controllability counterexamples in are generalized to arbitrary finite-dimensional cases.