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Fixed-time stabilization of second-order uncertain multivariable nonlinear systems

Abstract : This paper studies the fixed-time stabilization problem for a class of second-order multivariable multi-input nonlinear systems with matched uncertainties. Different from the control design for scalar systems, a multivariable sliding mode control design, based on a set of nonlinear coupled sliding surfaces, is proposed to stabilize the system at the origin with a uniformly bounded settling time, i.e., fixed-time stabilization. The key benefit of the proposed design framework is the reduction of discontinuity and singularity. For practical implementation, a saturation function is injected into the proposed design to avoid the control singularity problem, and an almost fixed-time stability of the resultant system is proved by using the phase analysis and the Lyapunov tools. Finally, a two-link planar elbow robot is introduced as an example to validate the effectiveness of our design framework.
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https://hal-uphf.archives-ouvertes.fr/hal-03406837
Contributor : Mylène Delrue Connect in order to contact the contributor
Submitted on : Thursday, October 28, 2021 - 10:05:13 AM
Last modification on : Wednesday, November 3, 2021 - 3:56:50 AM

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Zongyu Zuo, Michael Defoort, Bailing Tian, Zhengtao Ding. Fixed-time stabilization of second-order uncertain multivariable nonlinear systems. 2016 35th Chinese Control Conference (CCC), Jul 2016, Chengdu, China. pp.907-912, ⟨10.1109/ChiCC.2016.7553202⟩. ⟨hal-03406837⟩

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