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In the real-world, self-driving vehicles are required to achieve steering maneuvers in both uncontrolled and uncertain environments while maintaining high levels of safety and passengers' comfort. Ignoring these requirements would inherently cause a significant degradation in the performance of the control system, and consequently, could lead to life-threatening scenarios. In this paper, we present a robust path following control of a self-driving vehicle under mismatched perturbations due to the effect of parametric uncertainties, vehicle side-slip angle, and road banking. In particular, the proposed control framework includes two parts. The first part ensures that the lateral and the yaw dynamics behave with nominal desired dynamics by canceling undesired dynamics. The second part is composed of two extended high-gain observers to estimate the system state variables and the perturbation terms. Our stability analysis of the closed-loop systems confirms exponential stability properties under the proposed control law. To validate the proposed control system, the controller is implemented experimentally on an autonomous vehicle research platform and tested in different road conditions that include flat, inclined, and banked roads. The experimental results show the effectiveness of the controller, they also illustrate the capability of the controller in achieving comparable performance under inclined and banked roads as compared to flat roads under a range of longitudinal velocities.