Nonlinear Hamiltonian Systems Under Sampling

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits discrete-time representation in terms discrete gradient, with same energy function but modified damping and interconnection matrices. By construction, proposed sampled-data guarantees matching both state evolutions energy-balance at all sampling instants. Its generalization port-controlled leads characterize new power conjugate output so recovering concept average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation approach confirmed by its formulation Dirac formalism. Two classical examples are worked out validate modeling comparative way literature.