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Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions
journal contributionposted on 2023-06-07, 21:55 authored by Peter GieslPeter Giesl
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.
JournalJournal of Approximation Theory
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- Mathematics Publications
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