Finite differences in homogeneous discontinuous control

Finite differences can be used for the estimation of arbitrary-order real-time derivatives producing an output-feedback controller from any finite-time-stable r-sliding homogeneous controller. The resulting controller is capable to control the output of any smooth uncertain SISO system of a known permanent relative degree r and is robust with respect to measurement errors. Variable sampling step feedback being applied, the controller preserves the utmost r-sliding accuracy corresponding to the minimal possible sampling step in the absence of noises, otherwise the tracking accuracy is proportional to the unknown magnitude of the noise.