For an inductor-capacitor-inductor (LCL) equipped high-speed permanent magnet synchronous machine (LCL-HSPMSM), the negative resonance frequency in the synchronous rotating frame poses a significant yet understudied challenge to the robustness of the adjustable-speed system. This article proposes a two-degree-of-freedom (2DOF) current control strategy that enhances the robustness of the system by maximizing its global stability margin. First, a mathematical model of an LCL-HSPMSM in the discrete-time domain is established, based on which the influence of both positive and negative resonance frequencies on the system stability is analyzed. Subsequently, a phase compensator and a phase gain are introduced to achieve active damping for both resonance frequencies. Additionally, a feedforward controller provides an extra DOF to mitigate the coupling between dq-axes currents, distinguishing it from the conventional control strategy. Consequently, a robust system resilient to parameter mismatches can be achieved. Finally, experimental verification of the robust control strategy is conducted on a 60kr/min LCL-HSPMSM prototype, where key parameters are varied from 0.3 to 3 times the nominal values.