Higher order sliding modes and arbitrary-order exact robust differentiation

An arbitrary-order finite-time-convergent exact robust differentiator is constructed based on higher-order sliding mode (HOSM) technique. Being used in a feedback together with previously proposed HOSM controllers, it produces a universal controller, formulated in input-output terms only, which causes the output of any uncertain smooth SISO minimum-phase dynamic system with known relative degree to vanish in finite time. That allows exact tracking of arbitrary real-time smooth signals. The control can be made arbitrarily smooth, providing for arbitrarily-high tracking-accuracy order with respect to the sampling step. Only one parameter is to be tuned.