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

摘要

Many methods exist to detect stable equilibrium points x* of nonlinear dynamical systems (x) over dot = f(x). Most of them also prove the existence of a neighborhood N of x* such that all trajectories initialized in N converge to x*. This paper provides a numerical method combining Lyapunov theory with interval analysis which makes to find a set N which is included in the attraction domain of x*. (C) 2014 Elsevier B.V. All rights reserved.