Efficient Lyapunov Function computation for systems with multiple exponentially stable equilibria

Recently a method was presented to compute Lyapunov functions for nonlinear systems with multiple local attractors [5]. This method was shown to succeed in delivering algorithmically a Lyapunov function giving qualitative information on the system's dynamics, including lower bounds on the attractors' basins of attraction. We suggest a simpler and faster algorithm to compute such a Lyapunov function if the attractors in question are exponentially stable equilibrium points. Just as in [5] one can apply the algorithm and expect to obtain partial information on the system dynamics if the assumptions on the system at hand are only partially fulfilled. We give four examples of our method applied to different dynamical systems from the literature.