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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 636878, 20 pages
Research Article

Discrete-Time Multioverlapping Controller Design for Structural Vibration Control of Tall Buildings under Seismic Excitation

1Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya (UPC), Avinguda Bases de Manresa 61-73, 08242 Manresa, Barcelona, Spain
2Department of Engineering, Faculty of Engineering and Science, University of Agder (UiA), 4898 Grimstad, Norway

Received 22 June 2012; Revised 9 September 2012; Accepted 10 September 2012

Academic Editor: Jun Hu

Copyright © 2012 Francisco Palacios-Quiñonero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, a computationally effective strategy to obtain multioverlapping controllers via the Inclusion Principle is applied to design discrete-time state-feedback multioverlapping LQR controllers for seismic protection of tall buildings. To compute the corresponding control actions, the proposed semidecentralized controllers only require state information from neighboring stories. This particular configuration of information exchange allows introducing a dramatic reduction in the transmission range required for a wireless implementation of the communication system. To investigate the behavior of the proposed semidecentralized multioverlapping controllers, a proper simulation model has been designed. This model includes semiactive actuation devices with limited force capacity, control sampling times consistent with the communication latency, time-delayed state information, and communication failures. The performance of the proposed multioverlapping controllers has been assessed through numerical simulations of the seismic response of a 20-story building with positive results.