Higher order sliding modes and arbitrary-order exact robust differentiation

A. Levant*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publication2001 European Control Conference, ECC 2001
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783952417362
StatePublished - 2001
Externally publishedYes
Event6th European Control Conference, ECC 2001 - Porto, Portugal
Duration: 4 Sep 20017 Sep 2001

Publication series

Name2001 European Control Conference, ECC 2001


Conference6th European Control Conference, ECC 2001


  • Non-linear Observers
  • Robust Filtering
  • Stabilization of Non-linear Systems
  • Trajectory Tracking in Non-linear Systems
  • Variable Structure Control


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