The paper presents a robust data-driven controller synthesis method for generalised multi-input multioutput (MIMO) systems. Using the frequency response of a linear time-invariant (LTI) MIMO system and characterising perturbations through Integral Quadratic Constraint (IQC), the method provides a convex set of controllers robust to perturbations. This facilitates the design of controllers with either robust stability or robust performance criteria. Notably, the proposed method is versatile, as it is also applicable for non-parametric IQC multipliers. An example of a non-parametric IQC multiplier for elliptical uncertainty quantification is demonstrated and subsequently employed in designing a robust controller for a hybrid active-passive micro-vibration platform. Experimental results show that the synthesised controller effectively achieves the desired levels of both robustness and performance.