Error analysis for a class of numerical differentiator: application to state observation

Da-Yan Liu (1, 2) , Olivier Gibaru (2, 3) , Wilfrid Perruquetti (2, 4)

1 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
2 ALIEN - Algebra for Digital Identification and Estimation
3 L2MA - Laboratoire de Métrologie et de Mathématiques Appliquées
4 SyNeR - Systèmes Non Linéaires et à Retards

In this note, firstly a modified numerical differentiation scheme is presented. The obtained scheme is rooted in the numerical differentiation method of Mboup M., Join C., Fliess M. and uses the same algebraic approach based on operational calculus. Secondly an analysis of the error due to a corrupting noise in this estimation is conducted and some upper-bounds are given on this error. Lastly a convincing simulation example gives an estimation of the state variable of a nonlinear system where the measured output is noisy.

Domaines: Analyse numérique [math.NA]; Automatique

Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti. Error analysis for a class of numerical differentiator: application to state observation. 48th IEEE Conference on Decision and Control, Dec 2009, Shanghai, China. ⟨inria-00437129⟩