A Lyapunov based Saturated Super-Twisting Algorithm

Ismael Castillo*, Martin Steinberger, Leonid Fridman, Jaime A. Moreno, Martin Horn

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Two different structures of saturated super-twisting algorithms are presented. Both structures switch from a relay controller to super-twisting algorithm through a switching law that is based on Lyapunov-level curves allowing the algorithms to generate bounded control signals. The relay controller provides a saturated control signal enforcing the system trajectories to reach a predefined neighborhood of the origin in which the super-twisting algorithm dynamics does not saturate, ensuring finite-time convergence to the origin. In order to increase the maximal admissible bound of the perturbations, the second algorithm also includes a perturbation estimator setting super-twisting’s integrator to the theoretically exact perturbation estimation. Experimental results are presented to validate the proposed algorithms.
Original languageEnglish
Title of host publicationEmerging Trends in Sliding Mode Control
EditorsAxaykumar Mehta, Bijnan Bandyopadhyay
PublisherSpringer Singapore
Number of pages22
Publication statusPublished - 1 Jan 2021

Publication series

NameStudies in Systems, Decision and Control
ISSN (Print)2198-4182
ISSN (Electronic)2198-4190


  • sliding mode control
  • saturated control
  • Super-twisting algorithm
  • Lyapunov methods
  • bounded control

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Control and Optimization
  • Decision Sciences (miscellaneous)
  • Economics, Econometrics and Finance (miscellaneous)
  • Control and Systems Engineering
  • Automotive Engineering
  • Social Sciences (miscellaneous)


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