TY - JOUR
T1 - An arbitrary-order exact differentiator with predefined convergence time bound for signals with exponential growth bound
AU - Gómez-Gutiérrez, David
AU - Aldana-López, Rodrigo
AU - Seeber, Richard
AU - Angulo, Marco Tulio
AU - Fridman, Leonid
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - fixed-time stability
KW - predefined-time
KW - prescribed-time
KW - unknown input observers
KW - online differentiators
KW - Unknown input observers
KW - Predefined-time
KW - Fixed-time stability
KW - Prescribed-time
KW - Online differentiators
UR - http://www.scopus.com/inward/record.url?scp=85151794443&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2023.110995
DO - 10.1016/j.automatica.2023.110995
M3 - Article
SN - 0005-1098
VL - 153
JO - Automatica
JF - Automatica
M1 - 110995
ER -