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.

中文翻译：

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具有预定义收敛时间的稳健精确微分器

考虑用有界二阶导数精确微分信号的问题。提出了一类微分器，它们在固定的，即有限的和均匀有界的收敛时间内收敛到这种信号的导数。导出的调整程序允许为此收敛时间分配任意的、预定义的上限。此外还表明，可以通过适当的调整使该界限任意紧密。该过程的有用性通过将其应用于众所周知的统一鲁棒精确微分器来证明，该微分器作为特殊情况包含在所考虑的微分器类中。