Closed-loop asymptotic stability for a nα-differentiator by means of a fractional dynamic control

This paper proposes a fractional observer-based sliding-mode control for a generalized n alpha-differentiator with the aim of achieving closed-loop asymptotic stability. The proposed methodology introduces a controller capable of dealing with unknown fractional derivatives of the estimation error. At the same time, it offers a solution to the chattering phenomenon that these type of controllers usually suffer from. Finally, some numerical results are presented with the end of analyzing and discussing the suggested approach.