Construction of a global Lyapunov function using radial basis functions with a single operator

Giesl, Peter (2007) Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete and Continuous Dynamical Systems - Series B, 7 (1). pp. 101-124. ISSN 1531-3492

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Abstract

We study the basin of attraction of an asymptotically stable equilibrium of a general autonomous ordinary differential equation. Sublevel sets of Lyapunov functions provide subsets of the basin of attraction. In this paper we construct a Lyapunov function by approximation via radial basis functions. We show the existence and the smoothness of a Lyapunov function with certain, given orbital derivative. By approximation of this Lyapunov function via its orbital derivative using radial basis functions we obtain a global Lyapunov function and can thus determine each compact subset of the basin of attraction.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 20:18
Last Modified: 10 Jul 2012 09:25
URI: http://sro.sussex.ac.uk/id/eprint/25286
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