TY - JOUR
T1 - Robust Exact Differentiator inspired Discrete-Time Differentiation
AU - Rüdiger-Wetzlinger, Maximilian
AU - Reichhartinger, Markus
AU - Horn, Martin
PY - 2021
Y1 - 2021
N2 - This paper 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 order 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 invariant set. Furthermore the performance of the proposed algorithm is evaluated via simulation studies
AB - This paper 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 order 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 invariant set. Furthermore the performance of the proposed algorithm is evaluated via simulation studies
KW - Asymptotic stability
KW - Convergence
KW - Discrete-time systems
KW - Eigenvalues and eigenfunctions
KW - Heuristic algorithms
KW - Perturbation methods
KW - Sliding mode control
KW - Stability criteria
KW - Stability of nonlinear systems
KW - Tuning
UR - http://www.scopus.com/inward/record.url?scp=85112209348&partnerID=8YFLogxK
U2 - 10.1109/TAC.2021.3093522
DO - 10.1109/TAC.2021.3093522
M3 - Article
SN - 0018-9286
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
ER -