An arbitrary-order exact differentiator with predefined convergence time bound for signals with exponential growth bound

David Gómez-Gutiérrez, Rodrigo Aldana-López*, Richard Seeber, Marco Tulio Angulo, Leonid Fridman

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

There is a growing interest in differentiation algorithms that converge in fixed time with a predefined Upper Bound on the Settling Time (UBST). However, existing differentiation algorithms are limited to signals having an nth order Lipschitz derivative. Here, we introduce a general methodology based on time-varying gains to circumvent this limitation, allowing us to design nth order differentiators with a predefined UBST for the broader class of signals whose (n+1)th derivative is bounded by a function with bounded logarithmic derivative. Unlike existing methods whose time-varying gain tends to infinity, our approach yields a time-varying gain that remains bounded at the convergence time. We show how this last property maintains exact convergence using bounded gains when considering a compact set of initial conditions and improves the algorithm’s performance under measurement noise.
Originalspracheenglisch
Aufsatznummer110995
Seitenumfang9
FachzeitschriftAutomatica
Jahrgang153
DOIs
PublikationsstatusVeröffentlicht - 2023

ASJC Scopus subject areas

  • Elektrotechnik und Elektronik
  • Steuerungs- und Systemtechnik

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