Due to the nonlinear characteristics of the vehicle speed system, its stability is difficult to control. This paper analyzes the stability and traceability of the vehicle speed system under nonlinear characteristics. A sliding mode control method of the nonlinear system state observation based on linear matrix inequalities (LMIs) is proposed. In the proposed control method, Lyapunov function is used as the control function to track the position and speed of the vehicle speed system in real time. In the design process of the controller, the successive scaling method (SSM) is designed to improve the tracking accuracy. The simulation results demonstrate that the sliding mode control can effectively track the position of the vehicle speed system, which has better stability and traceability for the nonlinear vehicle speed system.