The synthesis of optimal controllers for vibrational protection of large-scale structures with multiple actuation devices and partial state information is a challenging problem. In this paper, we present a design strategy that allows computing this kind of controllers by using standard linear matrix inequality optimization tools. To illustrate the main elements of the new approach, a five-story structure equipped with two interstory actuation devices and subjected to a seismic disturbance is considered. For this control setup, three different controllers are designed: an ideal state-feedback H ∞ controller with full access to the complete state information and two static output-feedback H ∞ controllers with restricted neighbouring state information. To assess the performance of the proposed controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations are conducted, using the full scale North-South El Centro 1940 seismic record as ground acceleration input. The obtained results indicate that, despite the severe information constraints, the proposed static output-feedback controllers attain a level of seismic protection that is very similar to that achieved by the ideal state-feedback controller with complete state information.