Design and analysis of a continuous hybrid differentiator

In this study, a continuous hybrid differentiator is presented based on a strong Lyapunov function. The differentiator design can not only sufficiently reduce the chattering phenomenon of derivative estimation by introducing a perturbation parameter, but the dynamical performances are also improved by adding linear correction terms to the non-linear ones. Moreover, strong robustness ability is obtained by integrating sliding-mode items and the linear filter. Frequency analysis is applied to compare the hybrid continuous differentiator with a sliding-mode differentiator. The merits of the continuous hybrid differentiator include the excellent dynamical performances, restraining noises sufficiently and avoiding the chattering phenomenon.