A Linear Differentiator Based on the Extended Dynamics Approach

In this article, we propose a new linear differentiator, called extended dynamics differentiator (EDD), by the extended dynamics approach. By a proper choice of extended dynamics, the EDD can make use of the prior signal dynamics as much as possible. As a result, the accuracy of the EDD can be improved greatly provided we have known some signal dynamics before signal differentiation. When all the signal dynamics are known, the EDD will reach zero derivative tracking error. When only some boundedness of the signal is known, which is the same as the most existing differentiators, the EDD will turn out to be a high-gain differentiator. When the known signal dynamics are between the two of them, the EDD can do its best in some sense. The EDD well posedness is proved mathematically and the corresponding theoretical results are validated by numerical simulations.