A First-Order Differentiator with First-Order Sliding Mode Filtering

Abstract

This paper proposes a sliding mode differentiator for estimating the first-order derivatives of noisy signals. The proposed differentiator can be seen as a version of Slotine et al.’s sliding mode observer extended with additional non-Lipschitzness. It behaves exactly as a first-order low-pass filter in the sliding mode and is globally convergent. Its discrete-time implementation is based on the implicit (backward) Euler discretization, which does not result in chattering. The differentiator is validated through some numerical examples.