×

The stabilization of variable coefficient multi-dimensional wave equation with boundary disturbance. (Chinese. English summary) Zbl 1340.35187

Summary: This paper is concerned with the stabilization of variable coefficient multi-dimensional wave equation with boundary disturbance, and the active disturbance rejection control approach is adopted in investigation. Firstly, the time varying high gain observer is applied to the system instead of a constant high gain observer, which deals with the peaking value problem effectively. Secondly, the existence and uniqueness of the solutions of variable coefficient multi-dimension wave equation are verified by using the semigroup theory. Finally, a time varying high gain observer is used to estimate the boundary disturbance and offset it by a state feedback, which makes the system stable.

MSC:

35L05 Wave equation
35B35 Stability in context of PDEs
PDFBibTeX XMLCite