On controllability and near-controllability of discrete-time inhomogeneous bilinear systems without drift

In this paper, controllability and near-controllability of discrete-time inhomogeneous bilinear systems without drift are studied. Necessary and sufficient conditions for controllability and near-controllability of the systems are respectively presented. In particular, algorithms for computing the control inputs to achieve the transition of a given pair of states for the controllable systems and nearly controllable systems are also provided. Examples are shown to demonstrate the conceptions and results of the paper.