Feedback vibration control of a base-isolated building with delayed measurements using h<inf>∞</inf> techniques

In this paper we address the problem of vibration reduction of buildings with delayed measurements, where the delays are time-varying and bounded. We focus on a convex optimization approach to the problem of state-feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control design. An appropriate Lyapunov-Krasovskii functional and some free weighting matrices are used to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities (LMIs). The controller, which guarantees asymptotic stability and an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated through the simulation of an n-story base-isolated building.