This paper investigates a mixed traffic system consisting of a number of human-driven vehicles (HDVs) and connected and automated vehicles (CAVs) travelling on a single-lane ring-road. The dynamics of HDVs are described by the optimal velocity model. A nonlinear system's stability crucially relies on the size of the region of attraction associated with the stabilized equilibrium. Our research aims to design a controller that stabilizes the system while simultaneously enlarging the region of attraction. Enlarging the region of attraction provides enhanced guarantees for the overall stability of the system.