Finite-Time Vibration Control of Earthquake Excited Linear Structures with Input Time-Delay and Saturation

The problem of finite-time vibration control of earthquake excited linear structures with input time-delay and saturation is concerned in this paper. The objective of designing controllers is to guarantee the finite-time stability of closed-loop systems while attenuating earthquake-induced vibration of the structures. First, based on matrix transformation, the structural system is described as a state-space model, which contains actuator saturation and input time-delay. Then, based on a Lyapunov functional and finite-time stability analysis method, some sufficient conditions for the existence of saturation-tolerant finite-time vibration-attenuation controllers are obtained. By solving these conditions, the desired controllers can be obtained for the closed-loop system to be finite-time stable with a prescribed level of disturbance attenuation. It is shown by the simulation results that compared with some Lyapunov asymptotic stability results, finite-time stability control can result in better state responses. Furthermore, saturation-tolerant controller can result in a much lower controller gain than the ones without considering actuator saturations.