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

Giesl, Peter (2008) Construction of a local and global Lyapunov function using radial basis functions. IMA Journal of Applied Mathematics, 73 (5). pp. 782-802. ISSN 0272-4960

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Abstract

The basin of attraction of an asymptotically stable fixed point of the discrete dynamical system given by the iteration xn+1=g(xn) can be determined through sublevel sets of a Lyapunov function. In Giesl [On the determination of the basin of attraction of discrete dynamical systems. J. Difference Equ. Appl. 13(6) (2007) 523¿546] a Lyapunov function is constructed by approximating the solution of a difference equation using radial basis functions. However, the resulting Lyapunov function is non-local, i.e. it has no negative discrete orbital derivative in a neighborhood of the fixed point. In this paper we modify the construction method by using the Taylor polynomial and thus obtain a Lyapunov function with negative discrete orbital derivative both locally and globally.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 20:40
Last Modified: 25 Apr 2012 13:41
URI: http://sro.sussex.ac.uk/id/eprint/27345
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