Non-collocated control of an anti-stable system of coupled strings under delayed displacements/velocities feedback

Abstract

In this paper, we consider the non-collocated stabilization of three coupled wave equations with different speeds and joint anti-dampings. These anti-dampings put all eigenvalues of the system in the right complex plane. By designing two invertible transformations, the wave system is converted into an equivalent system with damping terms at the joint points. The feedback controllers with displacements/velocities are designed to obtain the target system. The well-posedness and exponential stability of the closed-loop system are established using the PDE approach, based on the exponential stability of the target system. Simulation results are presented to verify the effectiveness of the feedback control law.