Discrete Sliding-Mode-Based Differentiators

© 2016 IEEE. Sliding-mode-based differentiators of the input (t) of the order k yield exact estimations of the derivatives ,..., (k), provided an upper bound of |(k+1)(t)| is available in real-time. Practical application involves discrete noisy sampling of 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.