On the characterization of Hamiltonian systems via differential input-output equations

A result of P.E. Crouch and F. Lamnabhi-Lagarrigue (1988) which characterizes Hamiltonian systems described by second-order single-input single-output (SISO) input-output differential equations is extended. A general formalism that defines the adjoint variational equations from the input-output differential equation representation is given. This is used to characterize Hamiltonian systems by using the general results of P.E. Crouch and A.J. van der Schaft (1987), i.e., Hamiltonian systems are those systems for which the variational and adjoint variational systems coincide.<>