Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

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The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.
Original languageEnglish
Pages (from-to)924-929
JournalIEEE Control Systems Letters
Issue number4
Publication statusPublished - 2019
Event58th Conference on Decision and Control - Nice, France
Duration: 11 Dec 201913 Dec 2019


  • Sliding mode control
  • Convergence time
  • Lyapunov functions
  • Optimisation
  • Linear matrix inequalities
  • optimization
  • convergence time
  • LMIs
  • Variable-structure/sliding-mode control

ASJC Scopus subject areas

  • Control and Optimization
  • Control and Systems Engineering


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