A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm

Richard Seeber, Martin Horn, Leonid Fridman

Research output: Contribution to journalArticlepeer-review


The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or Hölder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.
Original languageEnglish
Pages (from-to)4301-4308
JournalIEEE Transactions on Automatic Control
Issue number12
Publication statusPublished - 2018


  • Lyapunov function
  • Reaching time
  • Sliding mode control

Fields of Expertise

  • Information, Communication & Computing


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