Discrete-time implementation of high-gain observers for numerical differentiation

High-gain observers have been used in non-linear control to estimate deriva tives of the output. In this paper, we study discrete-time implementation o f high-gain observers and their use as numerical differentiators, in noise- free as well as noisy measurements. We show that discretization using the b ilinear transformation method gives better results than other discretizatio n methods. We also show that many of the available numerical differentiator s are special cases of the bilinear discrete-time equivalents of full-order or reduced-order high-gain observers.