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

Abstract

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.