Study of a Class of Almost-controllable Discrete-time Bilinear Systems

This paper studies the controllability of a class of time-invariant discrete-time bilinear systems. Although the system is not controllable in the whole space, there is a very large region where control is effective. Results show that the uncontrollable region of this kind of bilinear system has a Lebesgue measure of zero. In other words, for almost any initial state and any terminal state in the state space, the former can be transferred to the latter. Further, a necessary condition for near controllability is presented. Therefore, the results in this paper unify and generalize the corresponding conclusions in the literature. (c) 2014 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd