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Generating new classes of fixed-time stable systems with predefined upper bound for the settling time

Abstract : This paper aims to provide a methodology for generating autonomous and non-autonomous systems with a fixed-time stable equilibrium point where an Upper Bound of the Settling Time (UBST) is set a priori as a parameter of the system. Furthermore, some conditions for such an upper bound to be the least one are provided. This construction procedure is a relevant contribution compared with traditional methodologies for generating fixed-time algorithms satisfying time constraints since current estimates of an UBST may be too conservative. The proposed methodology is based on time-scale transformations and Lyapunov analysis. It allows the presentation of a broad class of fixed-time stable systems with predefined UBST, placing them under a common framework with existing methods using time-varying gains. To illustrate the effectiveness of our approach, we generate novel, autonomous and non-autonomous, fixed-time stable algorithms with predefined least UBST.
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https://hal-uphf.archives-ouvertes.fr/hal-03716501
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Submitted on : Thursday, July 7, 2022 - 3:01:31 PM
Last modification on : Friday, July 8, 2022 - 4:15:20 AM

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Rodrigo Aldana-Lopez, David Gomez-Gutierrez, Esteban Jiménez-Rodríguez, Juan Diego Sanchez-Torres, Michael Defoort. Generating new classes of fixed-time stable systems with predefined upper bound for the settling time. International Journal of Control, Taylor & Francis, 2021, pp.1-13. ⟨10.1080/00207179.2021.1936190⟩. ⟨hal-03716501⟩

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