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

Recently, a first-order differentiator based on time-varying gains was introduced in the literature, in its nonrecursive form, for signals having a second-order derivative bounded by a known time-varying function, where such time-varying bound has a logarithmic derivative bounded by a known constant. It has been shown that such differentiator is globally finite-time convergent. In this article, 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, but with guaranteed convergence before a desired time, that is, 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 related state-of-the-art algorithms.