I. Introduction
Sliding-modes are widely used to design and implement observer [1]–[4] due to their finite-time convergence, accuracy and robustness properties with respect to uncertainties [5]. One of its main disadvantages is the chattering effect [5]. An observer-based on sliding-modes is the high-order sliding mode homogeneous differentiator presented in [6]. It estimates the first derivatives of a signal if its order derivative has a known bound. Moreover, this differentiator has shown good robustness properties in the presence of noises, and exact finite-time convergence in the absence of noises. The structure of this observer has been implemented in different areas in [7]–[9].