In page 21 of this lecture note, quaternion error approximation for small errors has been defined as the deduction of the desired from current. It does not make sense mathematically speaking. However, it might be reasonable practically.
Hi Samira, in such cases it is often reasonible to linearize in order to have simple processing afterwards. However, this is equivalent with a restiction to (very) small angles. So it depends on your problem and the processing capabilities how to perform or how to proceed...