This research addresses the control challenges of underactuated re-entry vehicles by developing a lateral coupling control system. A linearized state-space representation is constructed to derive the system's transfer function and closed-loop characteristic equation. The controllability and observability of the system are assessed, confirming the feasibility of the pole placement method. This approach is implemented in the design of a underactuated control system, which is instrumental in ensuring swift tracking of the roll angle and effective rejection of side-slip disturbances. Based on a set of aerodynamic data from high-performance underactuated vehicles, the stability of the system is evaluated using the Routh-Hurwitz criterion. The robustness of the underactuated control system is further validated against uncertainties in aerodynamics and actuators, demonstrating its potential for efficient and stable control in the application of high-performance re-entry vehicles.