Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial dynamical systems. Employment of a positive definite function called shape function within the Sum-of-Squares procedure helps to find a richer representation of the Lyapunov function and a larger corresponding Region of Attraction estimation. However, existing Sum-of-Squares opti…