# Inferring Global Exponential Stability Properties using Lie-bracket Approximations

arXiv: https://arxiv.org/abs/2409.03871 · HTML: https://mlsanity.com/paper/2409.03871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [A Physics-Inspired Optimizer: Velocity Regularized Adam](https://mlsanity.com/paper/2505.13196/) (2025)

## Abstract (arXiv)

In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to their associated Lie-bracket systems is shown. The result is applied to adapt dither frequencies to find a sufficiently high gain in adaptive control of linear unknown systems, and a simple numerical example is simulated to support the theoretical findings.