Abstract
In this paper, we consider the stabilization problem of two coupled wave equations with joint anti-damping. By designing a novel transformation, the wave system is transformed into a system with damping term at the joint point, and the feedback controller with delayed displacement is designed. The invertibility of the transformation is proven through the mathematical induction. Furthermore, by using the Riesz basis method and the PDE approach, the well-posedness and exponential stability of the non-dissipative closed-loop system are established. Simulation results are presented to verify the effectiveness of the feedback control law.
| Original language | English |
|---|---|
| Article number | 129616 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 551 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Nov 2025 |
| Externally published | Yes |
Keywords
- Delayed displacement
- Exponential stability
- Joint anti-damping
- Non-collocated control