This paper describes the development of the $H_{infty}$ lateral control system for an autonomous ground vehicle operating a limited area using the RTK-DGPS(Real Time Kinematic-Differential Global Positioning System). Before engaging in autonomous driving, map data are acquired by the RTK-DGPS and used to construct a reference trajectory. The navigation system contains the map data and computes the reference yaw angle of the vehicle using two consecutive position values. The yaw angle of the vehicle is controlled by the $H_{infty}$ controller. A prototype of the autonomous vehicle by the navigation method has been developed, and the performance of the vehicle has been evaluated by experiment. The experimental results show that the $H_{infty}$ controller and the RTK-DGPS based navigation system can sufficiently track the map at low speed. We expect that this navigation system can be made more accurate by incorporating additional sensors.