Robust exact differentiators with predefined convergence time

TL;DR

This paper introduces a class of robust exact differentiators that guarantee finite, predefined convergence time, with a tuning method to make this bound arbitrarily tight, enhancing signal differentiation accuracy.

Contribution

It proposes a new class of differentiators with fixed convergence time and a tuning procedure to optimize this bound, improving upon existing methods.

Findings

Differentiators converge within a predefined finite time.

Tuning allows the convergence bound to be made arbitrarily tight.

Application to known differentiators demonstrates the method's effectiveness.

Abstract

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.