<p>This paper develops a formulation of linear matrix inequalities (LMIs) for data-driven path following control of an unmanned surface vehicle (USV) subject to partially unknown dynamics. The proposed formulation is to decompose the whole system into a fully known guidance-error subsystem and sway yaw dynamics with the partially unknown components, rather than treating it as unknown. These unknown components are constrained to a data-consistent, matrix-ellipsoidal uncertainty set inferred from input state measurements, thereby avoiding explicit parameter identification. Sufficient conditions in the form of LMIs are derived to guarantee robust asymptotic stability of the associated closed-loop system under a matrix-ellipsoidal uncertainty set. An example is provided to examine that the proposed data-driven controller achieves the path-following performance comparable to that of a fully model-based controller across diverse reference paths.</p>