The basin of attraction of an equilibrium can be determined using a contraction metric, which has the advantage of being robust with respect to perturbations of the system. Recently, a novel numerical method to compute and verify a contraction metric was proposed, but so far it has only been applied to two-dimensional systems. In this paper, we apply the method to three-dimensional systems and determine a subsets of their basins of attraction and investigate the sensitivity to perturbations.
Giesl, P., Hafstein, S., Mehrabi Nezhad, I. (2021). Computing Contraction Metrics for three-dimensional systems. In IFAC-PapersOnLine (pp.297-303). Elsevier B.V. [10.1016/j.ifacol.2021.06.151].
Computing Contraction Metrics for three-dimensional systems
Mehrabi Nezhad I.
2021
Abstract
The basin of attraction of an equilibrium can be determined using a contraction metric, which has the advantage of being robust with respect to perturbations of the system. Recently, a novel numerical method to compute and verify a contraction metric was proposed, but so far it has only been applied to two-dimensional systems. In this paper, we apply the method to three-dimensional systems and determine a subsets of their basins of attraction and investigate the sensitivity to perturbations.
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