Arbitrary order differentiator with varying homogeneity degree. (April 2022)

• Record Type: Journal Article
• Authors: Ghanes, Malek; Moreno, Jaime A.; Barbot, Jean-Pierre
• Is Part Of: Automatica. Volume 138(2022)
• Publication Date: 2022-04
• Subjects: Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.110111
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper, we propose an arbitrary order differentiator with time-varying homogeneity degree (exponent) and we establish its convergence properties and its robustness with respect to measurement noise, perturbations and the variation of the exponent. For this we use a unified Lyapunov function approach. We also propose two possible applications for such a differentiator. One provides a variation of the exponents that ensures a differentiator converging in fixed and finite times . The other that extends our previous results, aims at improving the behavior of the differentiator with respect to measurement noise, for which a noise-driven variation of the exponents is given. The results are illustrated using simulations for a second order differentiator.