Linearization of discrete-time nonlinear systems through state immersion and Lie symmetries *

In this paper, it is shown that if a discrete-time nonlinear system admits a Lie symmetry that can be linearized by a state diffeomorphism, then, under some technical conditions, such a discrete-time nonlinear system can be immersed into a linear one, thus generalizing a similar result valid for continuous-time nonlinear systems.