The instability of the car-trailer systems very often leads to the snaking and/or rocking motions of trailers. In order to reduce the safety risk of these unwanted vibrations, stability control can be applied. In this paper, we use a spatial trailer model to analyze the effect of a possible control algorithm, which actuates by means of braking. For the sake of simplicity, the dynamics of the towing vehicle is modeled by the lateral displacement of the tow hitch that is supported laterally by a spring and damper. The longitudinal speed of the vehicle is kept constant. The effect of the braking forces are emulated in our study via a control torque, which is proportional to the yaw angle and the yaw rate. The time delay of the controller is also considered. Linear stability charts are constructed in the plane of the different system parameters. Linearly stable and unstable parameter domains are identified both for the vertical position of the center of gravity and the control gains. Numerical simulations are used to validate the theoretical results.