In this work, we provide a tracking controller formulation for dynamically positioned surface vessels with an asymmetric added mass terms that affects the overall system dynamics at the acceleration level. Specifically a novel continuous robust controller is proposed for surface vessels that in addition to unstructured uncertainties in its dynamics, contains added mass effects in its inertia matrix. The proposed. controller compensates the overall system uncertainties while ensuring asymptotic tracking by utilizing the knowledge of the leading principal minors of the input gain matrix. Stability of the closed loop system and asymptotic convergence are proven via Lyapunov based approaches. Simulation studies are also presented to illustrate the viability of the proposed method.