Boundary Feedback Stabilization of Three Coupled Strings with Joint Anti-Dampers

In this paper, we are concerned with the stabilization of three connected strings with joint anti-dampers. By two equivalent transformations, we propose a boundary output feedback law with non-collocated measurements. By the spectral analysis, we conclude that all eigenvalues of the closed-loop system are located on the left-half complex plane. We prove the well-posedness and the Riesz basis property of the closed-loop system. Then the spectrum-determined growth condition of the closed-loop system is established. We conclude that the closed-loop system is exponentially stable.