Robust-Exact-Differentiator-Inspired Discrete-Time Differentiation

This article proposes a discrete-time differentiation algorithm of arbitrary order inspired by the continuous-time uniform robust exact differentiator and the continuous-time arbitrary-order robust exact differentiator. As the well-known explicit Euler method is not suitable for discretizing algorithms with the fixed-time convergence property, a semi-implicit approach is proposed. The discrete-time differentiators of orders 2 and 3 are studied in detail, and it is proven that the estimation errors vanish independent of their initial condition in the unperturbed case. In the presence of perturbations, it is shown that the origin of the estimation errors is surrounded by an attractive set. Furthermore, the performance of the proposed algorithm is evaluated via simulation studies.