Generalised multivariable supertwisting algorithm. (English) Zbl 1411.93097
Summary: The purpose of this paper is to present an extension of the generalized 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 characterize 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 generalized multivariable STA. Furthermore, the class of finite-time stable systems comprise the currently available versions of STAs. To finalize, 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.
MSC:
| 93C35 | Multivariable systems, multidimensional control systems |
| 93D09 | Robust stability |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B40 | Computational methods in systems theory (MSC2010) |
| 93B12 | Variable structure systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
differentiator; fixed-time stability; Lyapunov stability; multivariable supertwisting algorithm; second-order sliding modesReferences:
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