Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions

@article{Giesl2008ConstructionOA,
  title={Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions},
  author={Peter Giesl},
  journal={Journal of Approximation Theory},
  year={2008},
  volume={153},
  pages={184-211}
}
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 [3] 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… CONTINUE READING
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