Exact differentiators with assigned global convergence time bound

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 bound for this convergence time. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which the considered class of differentiators includes as a special case. Simulations show that the convergence time bounds thus assigned may exceed the actual worst-case convergence time by a factor of not more than four.

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