On a new sliding-mode differentiation scheme

We propose a new real-time differentiator, called the discontinuous high-gain observer (DHGO), which is derived from the classical HGO structure by introducing a discontinuous error term. Non-smooth Lyapunov analysis shows that the DHGO is a "theoretically-exact" differentiator in the absence of noise, meaning that the origin of the error state-space is a globally stable equilibrium point. A simulative comparison with the classical HGO and the 'Super-Twisting" second-order sliding mode differentiator has been carried out. Simulations results point out that the new proposed differentiator features a particularly effective trade-off between accuracy and noise immunity.