Controlling a vessel in the presence of constant, unknown disturbances requires control methods capable of adjusting to this situation. In this paper we use the multivariable circle criterion, extended to linear time-varying systems, and propose a method for curved trajectory tracking based on conditional integrators. This control method combines the robustness of sliding mode control and integral action, while avoiding their inherent drawbacks like chattering and integrator wind-up. The problem of curved trajectory tracking in the horizontal plane is discussed, showing a separation between the design of the tracking control law and the disturbance rejection control law. Simulation results are provided to illustrate the effectiveness of the proposed method.