High-speed regimes allow to increase the power density of electrical drives, which is a necessary characteristic in aeronautical applications. In such a context, together with the typical non-linearities of low speed drives, i.e., core saturation, phenomena related to high fundamental to sampling frequency ratios appear increasingly significant. This paper applies methodologies based on modern robust control to high-speed synchronous reluctance machines. The proposed method is based on a reformulation of the motor model as a linear parameter varying system. This allows transforming the current controller design in a multivariable optimization problem, which is solved with efficient numeric tools. The mathematical formulation of a robust digital controller directly designed in the discrete time domain is proposed. The controller performance are experimentally compared to those of its counterpart designed in the continuous time domain and subsequently discretized, as proposed in a previous work by the same authors, and to those of a more standard decoupled current control using PI regulators. Results demonstrate the effectiveness of the proposed controller structure in current regulation, especially at high-speed regimes.