Symmetries and conservation laws for Hamiltonian Systems with inputs and outputs:A generalization of Noether's theorem

The definitions of symmetries and conservation laws for autonomous (i.e. without external forces) Hamiltonian systems are generalized to Hamiltonian systems with inputs and outputs. It is shown that a symmetry implies the existence of a conservation law and vice versa; thereby generalizing Noether's theorem for autonomous Hamiltonian systems