In this paper, the challenge of asymptotically rejecting sinusoidal disturbances with unknown time-varying frequency and bounded rate is explored. A novel data-driven approach for designing linear parameter-varying (LPV) con- troller is introduced, leveraging only frequency domain data from a Linear Time Invariant (LTI) Multi-input Multi-output (MIMO) system, eliminating the need for a parametric model. A two-step iterative algorithm is proposed involving convex optimization problems in the frequency domain. Closed-loop stability is ensured using Integral Quadratic Constraints (IQC) that characterize the bounded rate variation of the LPV controller’s scheduling parameters. Experimental validation is provided through results obtained on a hybrid micro-vibration damping (MIVIDA) platform tailored for space applications.