  In this paper, a continuous hybrid differentiator is presented based on a
strong Lyapunov function. The differentiator design can not only reduce
sufficiently chattering phenomenon of derivative estimation by introducing a
perturbation parameter, but also the dynamical performances are improved by
adding linear correction terms to the nonlinear 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 sliding mode differentiator. The merits of the continuous
hybrid differentiator include the excellent dynamical performances, restraining
noises sufficiently, and avoiding the chattering phenomenon.
