The design of a controller for selective reduction of vibrations in flexible low-damped structures is presented. The objective of the active feedback control law is to increase damping of selected modes only, in frequency regions where a disturbance is likely to produce largest effect. Moreover, the stabilizing controller is required to be band-pass, in order to filter out high-frequency sensor noise and low-frequency accelerometer drift, and stable to increase robustness to uncertain parameters. The control design is based on the Inverse Optimal Design approach, through the solution of a matrix Stein equation, resulting in the solution of an optimal H-infinity control problem. A grey-box identification approach of the authors is employed for obtaining the model from experimental data or from detailed Finite Element Model (FEM) simulators. The problem of optimal actuator/sensor location is also addressed. Detailed simulation results are provided to show the effectiveness of the strategy. (C) 2016 Elsevier Ltd. All rights reserved.