Path-following control is a critical technology for autonomous vehicles. However, time-varying parameters, parametric uncertainties, external disturbances, and complicated environments significantly challenge autonomous driving. We propose an iterative robust gain-scheduled control (RGSC) with a finite time horizon based on linear matrix inequality (LMI) approach to address this issue. Firstly, a refined polytopic linear parameter varying (LPV) model is designed to consider inevitable time-varying parameters. Then, using a set of inequalities and constraints derived from Lyapunov asymptotic stability and the minimization of the worst-case objective function, a novel iterative RGSC technique is proposed to address the over-conservatism. Further, an expanded 3D phase plane is applied to define envelope surfaces, elucidating the connection of stable vehicle operation boundaries. Lane change maneuver is performed in TruckMaker/ Xpack4-RapidECU joint HIL platform. Compared with the infinite time horizon method, the tracking accuracy of our finite controller is significantly improved by 18.15%, 16.68%,14.32%, and 35.65% in cornering stiffness, mass, road conditions, and measurement noise, respectively. Simulation results reveal that our method maintains enhanced control accuracy, robustness, and less conservatism despite minor stability deterioration. An experimental test is carried out on an autonomous bus. The results indicate that our finite RGSC method demonstrates efficient computational characteristics and impressive tracking performance and holds the potential for seamless integration into autonomous vehicle systems. The suggested technique provides crucial insight into better trade-offs among robustness-oriented, less-conservatism-oriented, and stability-oriented control for practical application.