  Flatness of sampled data systems can be characterized by a simple property.
They must admit the transformation to special representations, which are the
series or partial series connection of a Brunovsky normal form and a
complement. It is shown that this property follows from an integrability
condition, which must be met by the flat parametrization. The series
connections admit a simplification by reduction of the original problem to a
simpler one, which allows us to develop two algorithms, where the first version
delivers the flat outputs directly, but one has to solve linear PDEs or
nonlinear ODEs. But one gets the flat outputs directly. The second version
overcomes this problem, but one can only test the existence of flat outputs.
