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  • Autor
    • Seeber, Richard
    • Reichhartinger, Markus
    • Horn, Martin
  • TitelA Lyapunov Function for an Extended Super-Twisting Algorithm
  • Datei
  • DOI10.1109/TAC.2018.2794411
  • Persistent Identifier
  • Erschienen inIEEE Transactions on Automatic Control
  • Band63
  • Erscheinungsjahr2018
  • Heft10
  • Seiten3426-3433
  • LicenceCC BY-NC-ND
  • ZugriffsrechteCC-BY
  • Download Statistik249
  • Peer ReviewJa
  • AbstractRecently, an extension of the super-twisting algorithm for relative degrees m ≥ 1 has been proposed. However, as of yet, no Lyapunov functions for this algorithm exist. This paper discusses the construction of Lyapunov functions by means of the sum-of-squares technique for m = 1. Sign definiteness of both Lyapunov function and its time derivative is shown in spite of numerically obtained-and hence possibly inexact-sum-of-squares decompositions. By choosing the Lyapunov function to be a positive semidefinite, the finite time attractivity of the system's multiple equilibria is shown. A simple modification of this semidefinite function yields a positive definite Lyapunov function as well. Based on this approach, a set of the algorithm's tuning parameters ensuring finite-time convergence and stability in the presence of bounded uncertainties is proposed. Finally, a generalization of the approach for m > 1 is outlined.