An algorithm for computing a neighborhood included in the attraction domain of an asymptotically stable point

•An algorithm based on Lyapunov Theory is provided to compute a subset of the attraction domain of an equilibrium point.•A method based on interval arithmetic and the Hessian matrix is used to prove that a given real function is non negative.•The efficiency and applicability of the technique are checked by some examples.

Many methods exist to detect stable equilibrium points x∗x∗ of nonlinear dynamical systems ẋ=f(x). Most of them also prove the existence of a neighborhood NN of x∗x∗ such that all trajectories initialized in NN converge to x∗x∗. This paper provides a numerical method combining Lyapunov theory with interval analysis which makes to find a set NN which is included in the attraction domain of x∗x∗.