Robust exact differentiators with predefined convergence time

The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded convergence time. A tuning procedure is derived that allows to assign an arbitrary, predefined upper bound for this convergence time. It is furthermore shown that this bound can be made arbitrarily tight by appropriate tuning. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which is included in the considered class of differentiators as a special case. (C) 2021 The Author(s). Published by Elsevier Ltd.

Automated summary

This study explores a method for accurately differentiating signals with bounded second derivatives in a finite time, proposing a class of differentiators with controlled convergence speeds. It also introduces a tuning process to set an upper limit on convergence time, which can be made tighter through appropriate tuning. The usefulness of this procedure is demonstrated by applying it to a well-known exact differentiator, showcasing its practical applications.