Converse theorems on contraction metrics for an equilibrium

Giesl, Peter (2015) Converse theorems on contraction metrics for an equilibrium. Journal of Mathematical Analysis and Applications, 424 (2). pp. 1380-1403. ISSN 0022-247X

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Abstract

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.

Item Type: Article
Keywords: Stability; Basin of attraction; Contraction metric; Converse theorem
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Peter Giesl
Date Deposited: 09 Jan 2015 13:35
Last Modified: 09 Jan 2015 13:35
URI: http://sro.sussex.ac.uk/id/eprint/52028
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