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Mathematical Problems in Engineering
Volume 2014, Article ID 302565, 13 pages
Research Article

A Modified D-K Iteration Approach for the Decentralized Control of Civil Structures with Parametric Uncertainties

Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

Received 30 October 2013; Revised 10 December 2013; Accepted 11 December 2013; Published 13 March 2014

Academic Editor: Hamid Reza Karimi

Copyright © 2014 Chunxu Qu 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.


This paper presents a robust decentralized controller design method to suppress the vibration of civil structures with the consideration of parametric uncertainties. The decentralized controller design is motivated by the double homotopy approach, which approximates the bilinear matrix inequality (BMI) derived from bounded real lemma to linear matrix inequality (LMI), and gradually deforms a centralized controller to a decentralized controller. The centralized controller can be designed for the civil structures with the parametric uncertainties through D-K iteration method in μ synthesis, which can consider the diagonal block pattern of the uncertain matrix. This paper combines the double homotopy approach and D-K iteration method to design the robust decentralized controller for the civil structures with parametric uncertainties. The proposed method is validated numerically with a four-story building example.