Study on the controllability of a class of discrete-time bilinear systems

Whether the controllability of a continuous system keeps the consistency after discretisation is an important issue in engineering. Recently, a two-dimensional counterexample was constructed by Elliott for an uncontrollable bilinear system and showed that its discrete-time counterpart is, however, controllable. In this paper, a sufficient condition for controllability of a class of second order discrete-time bilinear systems is proposed, which extends the result given by Elliott to more general cases and therefore, deepens our understanding of controllability of bilinear systems. Furthermore, it is shown that the controllability counterexample does not exist if the dimension of such systems is greater than two.