A linear algebraic criterion for controllability of both continuous-time and discrete-time symmetric bilinear systems

This paper presents a necessary and sufficient condition for controllability of two-dimensional continuous-time and discrete-time symmetric bilinear systems. The presented condition is a linear algebraic version which is easy to apply and verify. In particular, for the continuous-time case, the necessary and sufficient condition can replace the classical Lie-algebraic one. For the discrete-time case, the necessary and sufficient condition is new.