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Construction of a local and global Lyapunov function using radial basis functions
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.
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Publication status
- Published
Journal
IMA Journal of Applied MathematicsISSN
0272-4960Publisher
Oxford University PressExternal DOI
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5Volume
73Page range
782-802Pages
31.0Department affiliated with
- Mathematics Publications
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- No
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- Yes
Legacy Posted Date
2012-02-06Usage metrics
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