Construction of a local and global Lyapunov function using radial basis functions

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作者：
Giesl, Peter [1 ]
机构：
[1] Department of Mathematics, University of Sussex, Mantell Building, Falmer, Brighton BN1 9RF, United Kingdom
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| 1600年 / Oxford University Press卷 / 73期
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The basin of attraction of an asymptotically stable equilibrium for an autonomous differential equation x = f(x) can be determined through sublevel sets of a Lyapunov function. In Giesl (2007; Discrete Contin. Dyn. Syst. Ser. B; 7; 101-124); a Lyapunov function is constructed by approximating the solution of a linear partial differential equation using radial basis functions. However; the resulting Lyapunov function is non-local; i.e. it has no negative orbital derivative in a neighbourhood of the equilibrium. In this paper; we modify the construction method by using the Taylor polynomial and thus obtain a Lyapunov function with negative orbital derivative both locally and globally. © The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved;
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