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.
Original language | English |
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Article number | 110995 |
Number of pages | 9 |
Journal | Automatica |
Volume | 153 |
DOIs | |
Publication status | Published - 2023 |
Keywords
- fixed-time stability
- predefined-time
- prescribed-time
- unknown input observers
- online differentiators
- Unknown input observers
- Predefined-time
- Fixed-time stability
- Prescribed-time
- Online differentiators
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Control and Systems Engineering