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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 510236, 9 pages
Research Article

Optimal Design of Complex Passive-Damping Systems for Vibration Control of Large Structures: An Energy-to-Peak Approach

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

Received 25 April 2014; Accepted 4 June 2014; Published 29 June 2014

Academic Editor: Shen Yin

Copyright © 2014 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.


We present a new design strategy that makes it possible to synthesize decentralized output-feedback controllers by solving two successive optimization problems with linear matrix inequality (LMI) constraints. In the initial LMI optimization problem, two auxiliary elements are computed: a standard state-feedback controller, which can be taken as a reference in the performance assessment, and a matrix that facilitates a proper definition of the main LMI optimization problem. Next, by solving the second optimization problem, the output-feedback controller is obtained. The proposed strategy extends recent results in static output-feedback control and can be applied to design complex passive-damping systems for vibrational control of large structures. More precisely, by taking advantages of the existing link between fully decentralized velocity-feedback controllers and passive linear dampers, advanced active feedback control strategies can be used to design complex passive-damping systems, which combine the simplicity and robustness of passive control systems with the efficiency of active feedback control. To demonstrate the effectiveness of the proposed approach, a passive-damping system for the seismic protection of a five-story building is designed with excellent results.