On the design of 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. In addition, some conditions for such an upper bound to be the least one are provided. This construction procedure is a relevant contribution when 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.

Please cite the publisher's version. For the publisher's version and full citation details see: https://doi.org/10.1080/00207179.2021.1936190 The following links provide access, for a limited time, to a free copy of the publisher's version: https://www.tandfonline.com/eprint/BMPX5CUSEVFJYHHPMEES/full?target=10.1080/00207179.2021.1936190

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• A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time
• On Parameter Selection of Nonsingular Predefined-time Terminal Sliding Mode With the Fixed-time Convergence Guarantee