Controllability and observability for affine nonlinear Hamiltonian systems

It is shown that an affine nonlinear Hamiltonian system is "controllable" if and only if it is "observable," in the sense that strong accessibility implies local weak observability and vice versa. Furthermore, it is shown that a nonminimal Hamiltonian system can be reduced to a locally weakly observable and strongly accessible system, in such a way that the reduced system is again Hamiltonian.