Giesl, Peter (2008) Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions. Journal of Approximation Theory, 153 (2). pp. 184-211. ISSN 0021-9045

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Abstract

The basin of attraction of an asymptotically stable fixed point of the discrete dynamical system given by the iteration x(n+1) = g (x(n)) 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 19:03
Last Modified:	01 May 2012 14:29
URI:	http://sro.sussex.ac.uk/id/eprint/19155

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