An exact and uniformly convergent arbitrary order differentiator

An arbitrary order differentiator that, in absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n - 1)-times is that its n-th derivative is uniformly bounded by a known constant. The new differentiator is obtained by combining the HOSM differentiator with an additional part that converges uniformly with respect to the initial conditions.