English

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.

Keywords

Cite

@article{arxiv.1404.3475,
  title  = {Linearization and exponential stability},
  author = {Hans Zwart},
  journal= {arXiv preprint arXiv:1404.3475},
  year   = {2014}
}

Comments

5 pages

R2 v1 2026-06-22T03:49:54.407Z