English

Dirty derivative stability in the frequency domain

Optimization and Control 2023-05-16 v1 Systems and Control Systems and Control

Abstract

Differentiation filters can be made proper by composition with a first-order low-pass filter at a desired bandwidth, resulting in a "dirty derivative." A stable closed-loop system that relies on output derivatives remains stable when the derivatives are replaced with dirty derivatives of sufficiently high bandwidth. I prove and generalize this fact by a frequency-domain argument.

Cite

@article{arxiv.2305.08737,
  title  = {Dirty derivative stability in the frequency domain},
  author = {Simon Kuang},
  journal= {arXiv preprint arXiv:2305.08737},
  year   = {2023}
}
R2 v1 2026-06-28T10:34:52.464Z