On the Discretization of a Class of Homogeneous Differentiators

This paper proposes explicit and implicit discrete-time realizations for a class of homogeneous sliding-mode-based differentiators. The proposed approach relies on the exact discretization of the continuous differentiator. Also, it is demonstrated that the proposed implicit discretization always exists, is non-anticipative and unique. A numerical simulation shows the better performance of the implicit scheme over the proposed and the referenced explicit implementations.