In this paper, a sliding mode controller based on linear matrix inequality(LMI) is designed to solve the path tracking problem for autonomous vehicle systems with mismatched uncertainties. Firstly, the nonlinear uncertain system model is established based on the vehicle kinematics and dynamics equations, taking into account the uncertainties caused by tire sideslip and random interference etc. Then, a linear sliding mode path tracking control method is proposed for the linearized model. Sufficient conditions for the existence of a linear sliding surface are obtained by the aid of LMIs, and an explicit formula for the existence of a linear sliding surface is presented, which guarantees the quadratic stability of the reduced-order system. Finally, under the serret-Frenet coordinate system, the effectiveness of the proposed method is verified. Simulation results show that the desired path is tracked accurately and robustly with the designed controller.