Linear matrix inequality-based vibration control of three-dimensional Euler–Bernoulli beam with external disturbance

In this paper, we address the LMI-based vibration control problem of a three-dimensional Euler–Bernoulli beam subject to external disturbance. First, the dynamics of the system is characterized by several partial differential equations (PDEs). Second, in order to realize the disturbance rejection, we propose the disturbance observers. Based on these, the boundary control protocols are designed via linear matrix inequality (LMI) method for suppressing elastic vibration. A significant feature of LMI is that the control gains can be efficiently solved by this method. Finally, some simulation examples illustrate the effectiveness of the proposed theoretical results.