A survey on the controllability of bilinear systems

Bilinear systems are a special class of nonlinear systems, which are widely existing in real world, such as engineering, economics, biology, ecology, etc. Among nonlinear systems, bilinear systems are thought to be the most close to linear systems. The study on such systems has passed through nearly half a century. For the fundamental property, the controllability of bilinear systems has received considerable attention, while the difficulties and challenges still remain. The purpose of this paper is to give a survey on the controllability of bilinear systems through the discussion on the controllability of continuous-time bilinear systems and discrete-time bilinear systems, respectively. Particularly, new results on the controllability are reported for discrete-time bilinear systems. Finally, some examples of controllable bilinear systems are provided.