Input-output finite-time stability of time-delay systems and its application to active vibration control

This paper addresses the problems of input-output finite-time stability (IO-FTS) analysis for linear time-delay systems and its application to active vibration control for structural systems with input delay. By employing the Lyapunov-like function method, a sufficient condition for the IO-FTS of the time-delay system is proposed. Then, based on the IO-FTS analysis result, a state feedback controller is designed for the structural system to attenuate the output response due to the exogenous disturbance. The controller design condition is presented in terms of a set of linear matrix inequalities (LMIs). Considering a practical earthquake excitation, a vibration-attenuation example is given to illustrate the effectiveness of the developed theory.