Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization cannot be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz continuity under approximate discretizations.
Cite
@article{arxiv.1612.08469,
title = {Is Lipschitz Continuity Preserved under Sampled-Data Discretization?},
author = {Masoud Abbaszadeh},
journal= {arXiv preprint arXiv:1612.08469},
year = {2020}
}