Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)A new approach for vibration reduction of flexible structures subject to damage is here proposed, based on modal H-infinity-norm control. Considering that structural damage provokes different effects on each vibration mode, the proposed method concentrates the control action on modes that are indeed suffering the worst damage consequences. For this purpose, a new modal 14, norm is introduced, weighing each mode according to control design convenience. Based on this norm, a regular H-infinity. controller design is applied, using the linear matrix inequality approach. Simulated and experimental results show significant advantages of the proposed methodology over the regular H-infinity. approach, including damage tolerance.607686CNPq [141621/2012-5]CAPES [12337/13-7]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)