Enlarging the Region of Attraction for Nonlinear Systems through the Sum-of-Squares Programming

In the present study‎, ‎a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system‎. ‎Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller through the State-Dependent Riccati Equation (SDRE)‎. ‎Consequently‎, ‎its process is defined in the form of Sum-of-Squares (SOS) optimization problem with control and non-control constraints‎. ‎Of note‎, ‎the proposed technique is effective in estimating the ROA for a nonlinear system functioning on polynomial or non-polynomial dynamics‎. ‎In the present study‎, ‎the application of the proposed scheme are shown by numerical simulations‎.