A predefined-time first-order exact differentiator based on time-varying gains

Abstract

Recently, a first-order differentiator based on time-varying gains was introduced in the literature, in its non recursive form, for a class of differentiable signals $y(t)$, satisfying $|\ddot{y}(t)|\le L(t-t_0)$, for a known function $L(t-t_0)$, such that $\frac{1}{L(t-t_0)}\left|\frac{dL(t-t_0)}{dt}\right|\le M$ with a known constant $M$. It has been shown that such differentiator is globally finite-time convergent. In this paper, we redesign such an algorithm, using time base generators (a class of time-varying gains), to obtain a differentiator algorithm for the same class of signals, with guaranteed convergence before a desired time, i.e., with fixed-time convergence with an a priori user-defined upper bound for the settling time. Thus, our approach can be applied for scenarios under time-constraints. We present numerical examples exposing the contribution with respect to state-of-the-art algorithms.

Please cite the publisher's version. For the publisher's version and full citation details see: https://doi.org/10.1002/rnc.5536. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions

References in corpus (1)

• On the design of non-autonomous fixed-time controllers with a predefined upper bound of the settling time