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

This work extends an earlier result which characterized Hamiltonian systems described by second order SISO input-output differential equations. A general formalism is given which defines the adjoint variational equations from the input-output differential equation representation. This is then used to characterize Hamiltonian systems by employing the general results: Hamiltonian systems are those systems for which the variational and adjoint variational systems coincide