Optimal robust exact first-order differentiators with Lipschitz continuous output
<|reference_start|>Optimal robust exact first-order differentiators with Lipschitz continuous output: The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This paper develops a first-order differentiator with the following combination of properties: robustness to measurement noise, exactness in the absence of noise, optimal worst-case differentiation error, and Lipschitz continuous output where the output's Lipschitz constant is a tunable parameter. This combination of advantageous properties is not shared by any existing differentiator. Both continuous-time and sample-based versions of the differentiator are developed and theoretical guarantees are established for both. The continuous-time version of the differentiator consists in a regularized and sliding-mode-filtered linear adaptive differentiator. The sample-based, implementable version is then obtained through appropriate discretization. An illustrative example is provided to highlight the features of the developed differentiator.<|reference_end|>
@article{aldana-lopez2024optimal,
    title={Optimal robust exact first-order differentiators with Lipschitz
  continuous output},
    author={Rodrigo Aldana-Lopez, Richard Seeber, Hernan Haimovich, and David
  Gomez-Gutierrez},
    journal={arXiv preprint arXiv:2404.05863},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.05863},
    primaryClass={eess.SY cs.SY}
}