Is Lipschitz Continuity Preserved under Sampled-Data Discretization?
arXiv:1612.084693 citationsh-index: 19
Originality Synthesis-oriented
AI Analysis
This is a theoretical result for researchers working on sampled-data control and nonlinear systems, but it is incremental as it addresses a specific property under approximate discretization.
The paper investigates whether Lipschitz continuity is preserved under approximate discretization of continuous-time nonlinear models, showing that it is not always preserved and providing conditions under which it can be maintained.
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.