Multivariable Super-Twisting Algorithm for Systems With Uncertain Input Matrix and Perturbations

Jaime A. Moreno, Hector Rios, Luis Ovalle, Leonid Fridman

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This article proposes a Lyapunov approach to the design of a multivariable generalized super-twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.

Original languageEnglish
Pages (from-to)6716-6722
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - 1 Dec 2022

Bibliographical note

Funding Information:
This work was supported in part by the CONACYT under Grant 282013, in part by PAPIIT-UNAM under Grant IN106622 and Grant IN102121.

Publisher Copyright:
© 1963-2012 IEEE.


  • Robust control
  • sliding-mode control
  • super-twisting algorithm
  • uncertain systems


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