  The paper addresses the exact linearization of flat nonlinear discrete-time
systems by generalized static or dynamic feedbacks which may also depend on
forward-shifts of the new input. We first investigate the question which
forward-shifts of a given flat output can be chosen in principle as a new
input, and subsequently how to actually introduce the new input by a suitable
feedback. With respect to the choice of a feasible input, easily verifiable
conditions are derived. Introducing such a new input requires a feedback which
may in general depend not only on this new input itself but also on its
forward-shifts. This is similar to the continuous-time case, where feedbacks
which depend on time derivatives of the closed-loop input - and in particular
quasi-static ones - have already been used successfully for the exact
linearization of flat systems since the nineties of the last century. For
systems with a flat output that does not depend on forward-shifts of the input,
it is shown how to systematically construct a new input such that the total
number of the corresponding forward-shifts of the flat output is minimal.
Furthermore, it is shown that in this case the calculation of a linearizing
feedback is particularly simple, and the subsequent design of a discrete-time
flatness-based tracking control is discussed. The presented theory is
illustrated by the discretized models of a wheeled mobile robot and a 3DOF
helicopter.
