An LMI approach to vibration control of base-isolated building structures with delayed measurements

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.