Transfer operator approach for computing domain of attraction

In this paper, we propose a linear transfer operator-based approach for the computation of domain of attraction of an attractor set. The almost everywhere notion of stability of an attractor set is used for the computation of domain of attraction. The proposed method is applicable to autonomous dynamical systems with the only requirement that the system mapping is a differentiable function of states. Furthermore domain of attraction of any general attractor set can be computed. Set oriented numerical scheme and iterative procedure based on the solution of finite dimensional linear program is proposed for the computation of domain of attraction. The application of the proposed method is demonstrated on two and three dimensional continuous and discrete-time systems.