Problem of tracking a reference with unknown derivatives

High-gain observers have been used as approximate differentiators in state estimation in nonlinear systems. The classical problem of tracking a reference signal requires knowledge of certain derivatives of the reference. This information may not be available on-line. We extend the use of high-gain observers to formulate special forms that estimate the requisite derivatives. The development is primarily based on tracking properties of thigh-gain observers, which have been termed as wide-band filters in this particular application. Related issues like estimation error have been discussed in the course of development. It has also been shown that step- and ramp-invariant discrete equivalents are the appropriate methods for implementation of wide-band filters.