Discrete Sliding-Mode-Based Differentiators

Jean-Pierre Barbot (1, 2) , Arie Levant (3) , Miki Livine (3) , Davin Lunz (4)

1 NON-A - Non-Asymptotic estimation for online systems
2 QUARTZ - Laboratoire QUARTZ
3 TAU - School of Mathematical Sciences [Tel Aviv]
4 University of Oxford

Sliding-mode-based differentiators of the input f(t) of the order k yield exact estimations of the derivatives f(1), … f(k), provided an upper bound of |f(k+1)(t)| is available in real time. Practical application involves discrete noisy sampling of f and numeric integration of the internal variables between the measurements. The corresponding asymptotic differentiation accuracies are calculated in the presence of Euler integration and discrete sampling, whereas both independently feature variable or constant time steps. Proposed discrete differentiators restore the optimal accuracy of their continuous-time counterparts. Simulation confirms the presented results.

Domaines: Automatique / Robotique

Jean-Pierre Barbot, Arie Levant, Miki Livine, Davin Lunz. Discrete Sliding-Mode-Based Differentiators. The 14th International Workshop on Variable Structure Systems (VSS 2016), Jun 2016, Nanjing, Jiangsu, China. ⟨hal-01338297⟩