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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.

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