Discretization of the Robust Exact Filtering Differentiator Based on the Matching Approach

This paper presents a time discretization of the robust exact filtering differentiator, a sliding mode differentiator coupled to filter, which provides a suitable approximation of the derivatives for some noisy signals. This realization rely on the stabilization of a pseudo linear discrete-time system, it is attained through the matching approach. As in the original case, the convergence of the robust exact filtering differentiator depends on the bound of a higher-order derivative. Nevertheless, this new realization can be implemented with or without the knowledge of such constant. It is demonstrated that the system trajectories converge to a neighborhood of the origin for a free-noise input. Finally, comparisons between the behavior of the differentiator with different design parameters are presented.ITESO, A.C