Levant’s differentiator by interconnection of low order blocks

摘要

On-line differentiation of (differentiable) signals is a central task in many engineering areas. Levant’s exact and robust differentiator is unique in the sense that it provides in finite-time the exact values of the derivatives of a signal with itsn—th derivative bounded. We propose here an alternative realization of this differentiator, by interconnecting low-order homogeneous differentiators that cooperate to supply in finite time and also exactly and robustly all derivatives of the signal. The proposed algorithm has a higher dimension than the original differentiator, and this extra dynamics seems to act as a noise filter. The result is illustrated by some simulations and the proof uses a novel Lyapunov function.