Controllability of discrete-time control system on the symplectic group. (Q5940772)

Let \(x_{n+1}=\exp(A+uB)x_{n}\) be a discrete-time control system on \(\mathbb R^{2n}\) with \(A\) and \(B\) matrices in the symplectic Lie algebra \(sp(n,R).\) This paper gives sufficient conditions for the global controllability of the system. These conditions are similar to those of \textit{Luiz A.B. San Martin} [ Math. Control Signals Syst. 8, No. 3, 279--297 (1995; Zbl 0853.93024)].