In this article, a computationally effective strategy to obtain multioverlapping controllers via the inclusion principle is applied to design a state-feedback multioverlapping linear-quadratic regulator controller for a 20-story building. The proposed semidecentralized controller only requires state information of neighboring stories to compute the corresponding control actions. This particular information exchange configuration allows introducing a dramatic reduction in the transmission range required for a wireless implementation of the communications system. More specifically, just a one-story transmission range is required by the proposed multioverlapping controller, while a full-building transmission range would be necessary in a classical centralized design. From a computational point of view, the presented design strategy only involves the actual computation of a reduced set of low-dimension controllers. The numerical simulations indicate that despite the simplified low-dimension design and the severe information exchange constraints, the proposed semidecentralized multioverlapping controller achieves a surprisingly high level of seismic attenuation when compared with the centralized linear-quadratic regulator controller.