In this paper, we investigate the State-Dependent Riccati Equation method to control nonlinear systems. This method stabilizes the closed loop system around the origin. However, global asymptotic stability is not ensured. Moreover, stability analysis is complicated because the closed loop system is typically not known in a closed form. We present a theorem that turns stability region estimation into a functional search problem. Results on sum of squares polynomials are used to turn this search into a semidefinite programming problem. A simple example demonstrating this method is given.