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.

中文翻译：

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基于扩展动力学方法的线性微分器


在本文中，我们通过扩展动力学方法提出了一种新的线性微分器，称为扩展动态微分器（EDD）。通过适当选择扩展动态，EDD 可以尽可能多地利用先前的信号动态。因此，只要我们在信号微分之前了解一些信号动态，就可以大大提高 EDD 的准确性。当所有信号动态已知时，EDD 将达到零导数跟踪误差。当仅知道信号的某些有界性时（与大多数现有微分器相同），EDD 将成为高增益微分器。当已知的信号动态介于两者之间时，EDD 在某种意义上可以发挥最大作用。从数学上证明了EDD的适定性，并通过数值模拟验证了相应的理论结果。