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