This paper studies the problem of linearizing the input-output map of
an analytic discrete-time nonlinear system locally around a given traj
ectory. Necessary and sufficient conditions are given for the existenc
e of a regular dynamic state feedback control law under which the inpu
t-dependent part of the response of a nonlinear system becomes linear
in the input and independent of the initial state. The proposed condit
ions are less restrictive than those obtained by Lee and Marcus for li
nearizing the input-output map via a static-state feedback. Instrument
al in the problem solution is the inversion (structure) algorithm for
a discrete-time nonlinear system. Firstly, the solvability conditions
are expressed in terms of the inversion algorithm. Secondly, the proof
of the existence and construction of the dynamic state feedback compe
nsator relies on this algorithm.