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Generalised multivariable supertwisting algorithm
Author(s) -
LópezCaamal Fernando,
Moreno Jaime A.
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4311
Subject(s) - multivariable calculus , stability (learning theory) , extension (predicate logic) , scalar (mathematics) , mathematics , class (philosophy) , algorithm , dynamical systems theory , lyapunov function , field (mathematics) , control theory (sociology) , computer science , nonlinear system , control (management) , artificial intelligence , engineering , control engineering , pure mathematics , physics , geometry , quantum mechanics , machine learning , programming language
Summary The purpose of this paper is to present an extension of the generalised supertwisting algorithm (STA) to the multivariable framework. We begin by introducing an algorithm that may be deemed as a linear, quasicontinuous, or discontinuous multivariable system, depending on the functions that define them. For the class represented by such an algorithm we prove the robust, Lyapunov stability of the origin and characterise the perturbations that preserve its stability. In particular, when its vector field is discontinuous or quasicontinuous our algorithm is endowed with finite‐time stability. Due to its resemblance to the scalar case, we denote such finite‐time stable systems as generalised multivariable STA . Furthermore, the class of finite‐time stable systems comprise the currently available versions of STAs. To finalise, by means of simulation examples, we show that our proposed finite‐time stable algorithms are well suited for signals online differentiation and highlight their dynamical traits.