On the estimation of asymptotic stability regions for autonomous nonlinear systems

The problem of computing regions of asymptotic stability forautonomous nolinear systems is reconsidered. A two-step procedureis proposed in which a suitable global Lyapunov function isfirst constructed to prove the system's nonoscillatory behaviour.Subsequently the Lyapunov function is used to compute the initialstates for a trajectory-reversing technique to estimate thesystem's stability boundaries. The method combines computationalefficiency and accuracy in obtaining a close estimate of theexact region of attraction of a stable equilibrium state.