Homogeneity approach to high-order sliding mode design

Arie Levant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

877 Scopus citations


It is shown that a general uncertain single-input-single-output regulation problem is solvable only by means of discontinuous control laws, giving rise to the so-called high-order sliding modes. The homogeneity properties of the corresponding controllers yield a number of practically important features. In particular, finite-time convergence is proved, and asymptotic accuracy is calculated in a very general way in the presence of input noises, discrete measurements and switching delays. A robust homogeneous differentiator is included in the control structure thus yielding robust output-feedback controllers with finite-time convergence. It is demonstrated that homogeneity features significantly simplify the design and investigation of a new family of high-order sliding-mode controllers. Finally, simulation results are presented.

Original languageEnglish
Pages (from-to)823-830
Number of pages8
Issue number5
StatePublished - May 2005


  • Discontinuous control
  • Finite-time stability
  • High-order sliding mode
  • Output feedback
  • Robustness


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