10-1016-j-jmaa-2014-12-010-post-ref-version.pdf (358.82 kB)
Converse theorems on contraction metrics for an equilibrium
The stability and basin of attraction of an equilibrium can be determined by a contraction metric. A contraction metric is a Riemannian metric with respect to which the distance between adjacent trajectories decreases. The advantage of a contraction metric over, e.g., a Lyapunov function is that the contraction condition is robust under perturbations of the system. While the sufficiency of a contraction metric for the existence, stability and basin of attraction of an equilibrium has been extensively studied, in this paper we will prove converse theorems, showing the existence of several different contraction metrics. This will be useful to develop algorithms for the construction of contraction metrics.
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- Published
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- Accepted version
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Journal of Mathematical Analysis and ApplicationsISSN
0022-247XPublisher
ElsevierExternal DOI
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2Volume
424Page range
1380-1403Department affiliated with
- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2015-10-29First Open Access (FOA) Date
2016-05-01First Compliant Deposit (FCD) Date
2015-10-29Usage metrics
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