Discrete-Time Implementations of Differentiators Homogeneous in the Bi-Limit

This chapter proposes a discrete-time differentiation algorithm of arbitrary order inspired by the uniform robust exact differentiator [1] and the generalized differentiator with negative homogeneity degree [2]. As the well-known explicit Euler method is not suitable for discretizing algorithms with the fixed-time convergence property, a semi-implicit discretizationSemi-implicit discretization and a stable explicit Euler discretization approach are proposed. It is proven that the proposed discrete-time algorithms are globally asymptotically stable in the unperturbed case for arbitrary order and converge to an attractive invariant set around the origin in the perturbed case. Furthermore the performance of the proposed algorithm is evaluated via simulation studies.