Sliding-Mode-Based Differentiation and Its Application

Sliding-mode (SM) based differentiation is exact on a large class of functions and robust to the presence of input noises. The best-possible differentiator accuracy is for the first-time calculated. A few differentiators and their discretizations are presented. As an important application of the differentiation technique we propose the first robust exact method for the estimation of the equivalent control and of a number of its derivatives from a SM control input.