On algebraic time-derivative estimation and deadbeat state reconstruction

TL;DR

This paper connects algebraic time-derivative estimation to deadbeat state reconstruction, showing that the former is a special case of the latter based on the reconstructibility Gramian, bridging two control theory approaches.

Contribution

It clarifies the relationship between algebraic derivative estimation and deadbeat state estimation, providing a theoretical perspective that unifies these methods.

Findings

Algebraic derivative estimation is a special case of deadbeat state estimation.

The connection is established through the reconstructibility Gramian.

The paper offers a theoretical insight into control system estimation methods.

Abstract

This note places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear state-space theory for control systems. In particular, it is shown that the algebraic method can in a sense be seen as a special case of deadbeat state estimation based on the reconstructibility Gramian of the considered system.