On convergence of nonlinear tracking differentiator based on finite-time stable system subject to stochastic noise

Abstract

In this paper, we consider convergence for a nonlinear tracking differentiator constructed from a finite-time stable system, where the input signal is corrupted by bounded stochastic noise. The existence of global weak solutions is firstly proved. It is shown that the nonlinear tracking differentiator tracks the input signal in the almost surely practical sense. With the same tuning parameter, the convergence accuracy is shown to be higher than that of the linear tracking differentiator. Some numerical simulations are performed to validate the effectiveness of the proposed differentiator.