Review Contraction Analysis P Giesl 15.2.22.pdf (775.03 kB)
Review on contraction analysis and computation of contraction metrics
journal contributionposted on 2023-06-10, 03:02 authored by Peter GieslPeter Giesl, Sigurdur Hafstein, Christoph Kawan
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the solutions under consideration. Using an appropriate metric, with respect to which the distance is contracting, one can show convergence to a unique equilibrium or, if attraction only occurs in certain directions, to a periodic orbit. Contraction analysis was originally considered for ordinary differential equations, but has been extended to discrete-time systems, control systems, delay equations and many other types of systems. Moreover, similar techniques can be applied for the estimation of the dimension of attractors and for the estimation of different notions of entropy (including topological entropy). This review attempts to link the references in both the mathematical and the engineering literature and, furthermore, point out the recent developments and algorithms in the computation of contraction metrics.
- Accepted version
JournalJournal of Computational Dynamics
PublisherAmerican Institute of Mathematical Sciences
Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
NotesThis article has been published in a revised form in Journal of Computational Dynamics http://dx.doi.org/10.3934/jcd.2022018 This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
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