FP9 = 16:20 ON THE CHARACTERIZATION OF HAMILTONIAN SYSTEMS VIA DIFFERENTIAL

This work extends a result of Crouch and Lainnabhi which characterized Hamiltonian sys-tems described by second order SISO input-output differential equations. A general for-malism is given which defines the adjoint vari-ational equations from the input-output differ-ential equation representation. This is then used to characterize Hamiltonian systems by employ-ing the general results of Crouch and van der Schaft: Hamiltonian systems are those systems for which the variational and adjoint variational systems coincide. 1 The adjoint system We consider state-space systems which may be written in the form e, x = f ( s, u) , y = I +) , (1) U E R'", y E R", and corresponding input-output representations F (y, j l,..., y ( N) , u, u,...,?AN- ' ) ) = 0. (2) If the system (1) is niinimal in the sense of Crouch and van der Schaft [a], the corresponding representation (2) will also be called a iiiininial representation. Note that we do not insist here on the relationship between state-space represen-tations (1) and input-output differential equa-tions representations (2). We assume that all conditions are met for obtaining one representa-tion from the other representation. See Sonta