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This paper presents a robust decentralized ℋ∞ controller design method to suppress the vibration of civil structures with the consideration of parametric uncertainties. The decentralized ℋ∞ 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 ℋ∞ 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 ℋ∞ controller for the civil structures with parametric uncertainties. The proposed method is validated numerically with a four-story building example

mathematical problems in engineering

A Modified<i>D-K</i>Iteration Approach for the Decentralized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℋ</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Control of Civil Structures with Parametric Uncertainties

A ModifiedD-KIteration Approach for the Decentralizedℋ∞Control of Civil Structures with Parametric Uncertainties