  The paper studies the relation between a nonlinear time-varying flat
discrete-time system and the corresponding linear time-varying systems which
are obtained by a linearization along trajectories. It is motivated by the
continuous-time case, where it is well-known that the linearization of flat
systems along trajectories results in linear time-varying systems which are
again flat. Since flatness implies controllability, this constitutes an
important verifiable necessary condition for flatness. In the present
contribution, it is shown that this is also true in the discrete-time case: We
prove that the linearized system is again flat, and that a possible flat output
is given by the linearization of a flat output of the nonlinear system.
Analogously, the map that describes the parameterization of the system
variables of the linear system by this flat output coincides with the
linearization of the corresponding map of the nonlinear system. The results are
illustrated by two examples.
