Is Lipschitz Continuity Preserved under Sampled-Data Discretization?
  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. 
Masoud Abbaszadeh
cs.SY cs.NA math.DS math.NA