Active vibration-attenuation controller design for uncertain structural systems with input time-delay

The problem of active vibration control for uncertain linear structural systems with control forces input timedelay is investigated in this study.First,the original structural equation is converted to a state-space model by utilizing the matrix transformation.Second,according to the obtained model and a special Lyapunov functional,a sufficient condition is achieved for the closed-loop system to be stable with a prescribed level of disturbance attenuation.Then,in terms of solving these linear matrix inequalities（LMIs）,the state-feed controller is achieved to stabilize the structural system with the performance ‖z‖2<γ‖ω‖2.Third,by introducing the rank-1 vector to describe the system uncertainties,the uncertain system description is obtained,and the stabilizing condition is extended to the uncertain case.Finally,examples are given to show the effectiveness of the proposed methods.