A Lyapunov Function for an Extended Super-Twisting Algorithm

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

Recently, 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.
Originalspracheenglisch
Seiten (von - bis)3426-3433
FachzeitschriftIEEE Transactions on Automatic Control
Jahrgang63
Ausgabenummer10
DOIs
PublikationsstatusVeröffentlicht - 2018

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Lyapunov functions
Tuning
Derivatives
Decomposition

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    A Lyapunov Function for an Extended Super-Twisting Algorithm. / Seeber, Richard; Reichhartinger, Markus; Horn, Martin.

    in: IEEE Transactions on Automatic Control, Jahrgang 63, Nr. 10, 2018, S. 3426-3433.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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    KW - Multiple equilibria

    KW - Polynomial methods

    KW - Positive semidefinite Lyapunov function

    KW - Sliding mode control

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