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This contribution deals with a new approach for computing Lyapunov functions represented by neural networks for nonlinear discrete-time systems to prove asymptotic stability. Based on the Lyapunov theory and the notion of domain of attraction, the proposed approach deals with an optimization method for determining a Lyapunov function modeled by a neural network while maximizing the domain of attraction. Several simulation examples are presented to illustrate the potential of the proposed method.

Computation of Neural Networks Lyapunov Functions for Discrete and Continuous Time Systems with Domain of Attraction Maximization