Levant’s Arbitrary Order Differentiator with Varying Gain

Abstract When the n-th derivative of a signal to be differentiated is bounded by a known constant, Levant’s arbitrary order differentiator provides, in the absence of noise, for an exact estimation of all derivatives up to order (n - 1) in finite time. Recently, Levant has shown that if the n-th derivative is bounded by a known time-varying function, the same differentiator with a time-varying gain is also able to estimate in finite time all derivatives, if the initial condition of the differentiation error is sufficiently small. In this paper we show, using a smooth Lyapunov function, that the same result is valid globally.

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