A Fourth Order Semi-Implicit Homogeneous Differentiator

Implicit discretization has many advantages over explicit discretization, especially for differential inclusion. Concerning sliding modes, the implicit discretization allows to reduce high frequency oscillations and ensures a larger stability domain. Nevertheless, it is not directly applicable to homogeneous differential equations and more particularly to homogeneous differentiators. This is why semi-implicit discretization methods have been developed in the literature. In this paper, we propose a semi-implicit discretization method with corrective terms for a homogeneous differentiator of order 4.