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Abstract
In this article, we address a convex optimisation approach to the problem of state-feedback H ∞ control design for vibration reduction of base-isolated building structures with delayed measurements, where the delays are time-varying and bounded. An appropriate Lyapunov–Krasovskii functional and some free-weighting matrices are utilised to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities. The controller, which guarantees asymptotic stability and an H ∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.
Acknowledgements
This study has been partially funded by the Norwegian Centre for Offshore Wind Energy (NORCOWE), the European Union (European Regional Development Fund) and the Ministry of Science and Innovation of Spain through the coordinated research projects DPI2008-06699-C02-01 and by the Government of Catalonia (Spain) through SGR523. M. Zapateiro is grateful for the grant of the Juan de la Cierva programme of the Ministry of science and Innovation (Spain).
