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A Lyapunov Function for an Extended Super-Twisting Algorithm.
- Source :
-
IEEE Transactions on Automatic Control . Oct2018, Vol. 63 Issue 10, p3426-3433. 8p. - Publication Year :
- 2018
-
Abstract
- Recently, an extension of the super-twisting algorithm for relative degrees $m\geq {}1$ 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 63
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 132099138
- Full Text :
- https://doi.org/10.1109/TAC.2018.2794411