File(s) not publicly available
Construction of a global Lyapunov function using radial basis functions with a single operator
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.
History
Publication status
- Published
Journal
Discrete and Continuous Dynamical Systems - Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
1Volume
7Page range
101-124Pages
24.0Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC