This paper presents the control of an autonomous vehicle using a Lyapunov-based technique with a LQR-LMI tuning. Using the kinematic model of the vehicle, a non-linear control strategy based on Lyapunov theory is proposed for solving the control problem of autonomous guidance. To optimally adjust the parameters of the Lyapunov controller, the closed loop system is reformulated in a linear parameter varying (LPV) form. Then, an optimization algorithm that solves the LQR-LMI problem is used to determine the controller parameters. Furthermore, the tuning process is complemented by adding a pole placement constraint that guarantees that the maximum achievable performance of the kinematic loop could be achieved by the dynamic loop. The obtained controller jointly with a trajectory generation module are in charge of the autonomous vehicle guidance. Finally, the paper illustrates the performance of the autonomous guidance system in a virtual reality environment (SYNTHIA) and in a real scenario achieving the proposed goal: to move autonomously from a starting point to a final point in a comfortable way.