In this article, vehicle cornering stability and brake stabilization via bifurcation analysis has been investigated. In order to extract the governing equations of motion, a nonlinear four-wheeled vehicle model with two degrees of freedom has been developed. Using the continuation software package MatCont a stability analysis based on phase plane analysis and bifurcation of equilibrium is performed and an optimal controller has been proposed. Finally, simulation has been done in Matlab-Simulink software considering a sine with dwell steering angle input, and the effectiveness of the proposed controller on the aforementioned model has been validated with Carsim model.