New types of high-speed nonlinear tracking differentiator with property analysis

Different from the existing high-speed nonlinear tracking-differentiator that applies the continuous-function combination of linearity and nonlinearity, this paper presents two new types of high-speed nonlinear tracking -differentiator which completely adopt continuous-function combination of nonlinearity. It is shown that the system state can rapidly converge to the equilibrium point no matter whether it is far away from the equilibrium point or near the equilibrium point. Since the switching control by switching functions is not used, the chattering phenomenon is avoided. Simulation results demonstrate the rapidness and efficiency of the designed nonlinear tracking-differentiators.