Linearization and exponential stability
Functional Analysis
2014-04-15 v1 Optimization and Control
Abstract
We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is Fr\'{e}chet differential at the equilibrium, if it is only Gateaux differentiable, then we show by means of an example that the result does not hold.
Cite
@article{arxiv.1404.3475,
title = {Linearization and exponential stability},
author = {Hans Zwart},
journal= {arXiv preprint arXiv:1404.3475},
year = {2014}
}
Comments
5 pages