This paper proposes a gray-box stability analysis mechanism based on data-driven dynamic mode decomposition (DMD) for commercial grid-tied power electronics converters with limited information on its control parameters and topology. By fusing the underlying physical constraints of the state equations into data snapshots, the system dynamic state matrix and input matrix are simultaneously approximated to identify the dominant system dynamic modes and eigenvalues using the DMD with control (DMDc) algorithm. While retaining the advantages of eliminating the need for intrinsic controller information, the proposed gray-box method establishes higher accuracy and interpretable outcomes over the conventional DMD method. Finally, under experimental conditions of a low-frequency oscillation scenario in electrified railways featuring a single-phase converter, the proposed gray-box DMDc is verified to identify the dominant eigenvalues more accurately.