In this paper, a new robust quadratic stable dynamic output feedback compensator is introduced and applied to a car steering model subject to parameter uncertainties. Arbitrary-order dynamic output feedback controllers are used together with the robust quadratic stabilization algorithm (RQSA) to attain a family of robust dynamic output compensators. A treatment through solving Lyapunov-like matrix equations and a special state transformation are employed. The RQSA is based only on checking end points of an uncertainty bounding hyperpolyhedron. The combined algorithm is implemented, and the simulations reveal that the new compensator provides more robust, stable and reliable performance under a variety of uncertainties involved in the car steering system model.