Mathematical control theory: deterministic systems
Mathematical control theory: deterministic systems
Error estimates for interpolation by compactly supported radial basis functions of minimal degree
Journal of Approximation Theory
A Generalization of Zubov's Method to Perturbed Systems
SIAM Journal on Control and Optimization
Radial Basis Functions
Meshless Collocation: Error Estimates with Application to Dynamical Systems
SIAM Journal on Numerical Analysis
Paper: Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems
Automatica (Journal of IFAC)
Computation of Lyapunov functions for smooth nonlinear systems using convex optimization
Automatica (Journal of IFAC)
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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.