A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time

Rodrigo Aldana-López; David Gómez-Gutiérrez; Marco Tulio Angulo; Michael Defoort

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arXiv · 2001.06707

A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time

Rodrigo Aldana-López·David Gómez-Gutiérrez·Marco Tulio Angulo·Michael Defoort

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Abstract

Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still lack a general methodology to design these algorithms for high-order perturbed systems when we additionally need to impose a user-defined upper-bound on their settling time, especially for systems with perturbations. Here, we fill this gap by introducing a methodology to redesign a class of asymptotically, finite- and fixed-time stable systems into non-autonomous fixed-time stable systems with a user-defined upper-bound on their settling time. Our methodology redesigns a system by adding time-varying gains. However, contrary to existing methods where the time-varying gains tend to infinity as the origin is reached, we provide sufficient conditions to maintain bounded gains. We illustrate our methodology by building fixed-time online differentiators with user-defined upper-bound on their settling time and bounded gains.

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Rodrigo Aldana-López, David Gómez-Gutiérrez, Marco Tulio Angulo, Michael Defoort. 2020-01-18. A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time. https://arxiv.org/abs/2001.06707

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