A robust decentralized control method based on dimensionless parameters with practical performance criterion for building structures under seismic excitations

A robust and decentralized control method for reducing vibration in a building, based on the Lyapunov-control function, is proposed and investigated. A new parameter that gives flexibility to the control design is introduced, and the control law is expressed in terms of dimensionless parameters. In addition, an expression adapted for semi-active control of which feedback gain is finite is proposed for a particular case. Analytical proof of the performance is completely derived for a system in which the control distribution matrix is not singular and a practical performance criterion is obtained. The influence of each parameter, along with the validity of the proposed performance criterion and the robustness to the uncertainties in the structural parameters, is extensively discussed with a single-degree-of-freedom numerical example. The performance of a decentralized system and the controller design in the case where the control distribution matrix is singular are discussed with a two-degree-of-freedom numerical application. A shaking table experiment using a small-scale model of a high-rise building with a vibration control device is conducted to verify the proposed method.