On the Variation of the Nonlinearity Parameter in the “Super-Twisting” Algorithm-Reference-Cited by-同舟云学术

On the Variation of the Nonlinearity Parameter in the “Super-Twisting” Algorithm

Published:2023-12-15 Issue:11 Volume:59 Page:1571-1574
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Fomichev V. V.¹²³,Vysotskiy A. O.²

Affiliation:

1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310005, China

2. Lomonosov Moscow State University, Moscow, 119991, Russia

3. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

Abstract

We study the stability of a modified (with variation in the nonlinearity parameter) “super-twisting” algorithm. The analysis is based on majorizing the trajectories of the system with an arbitrary nonlinearity parameter by the trajectories of systems of the classical “super-twisting” algorithm. Stability conditions for the modified systems are obtained, as well as estimates for the size of the stability domain depending on system parameters

Publisher

The Russian Academy of Sciences

Reference6 articles.

1. Емельянов С.В., Коровин С.К., Левантовский Л.В. Новый класс алгоритмов скольжения второго порядка // Мат. моделирование. 1990. Т. 2. № 3. С. 89-100.

2. Levant A. Sliding order and sliding accuracy in sliding mode control // Int. J. of Control. 1993. V. 58. P. 1247-1263.

3. Moreno J., Osorio M. Strict Lyapounov functions for the super-twisting algorithm // IEEE Trans. on Autom. Contr. 2012. V. 57. P. 1035-1040.

4. Seeber R., Horn M. Stability proof for a well-established super-twisting parameter setting // Automatica. 2017. V. 84. P. 241-243.

5. Seeber R., Horn M. Necessary and sufficient stability criterion for the super-twisting algorithm // 15th Intern. Workshop on Variable Structure Systems (VSS). 2018. P. 120-125.