Robust-Exact-Differentiator-Inspired Discrete-Time Differentiation

• 成果类型: Article
• 署名作者: Ruediger-Wetzlinger, Maximilian; Reichhartinger, Markus; Horn, Martin
• 署名单位: Graz University of Technology; Graz University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3093522
• 发表日期: 2022
• 页码: 3059-3066
• 关键词: Eigenvalues and eigenfunctions; CONVERGENCE; Heuristic algorithms; asymptotic stability; Tuning; Stability criteria; Perturbation methods; discrete-time systems; sliding-mode control; stability of nonlinear systems

摘要

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.