Stabilization of two coupled wave equations with joint anti-damping and non-collocated control

Abstract

In this paper, the non-collocated control problem of two connected wave equations with joint anti-damping is studied. The boundary dampings are introduced into the control at both ends of the boundary, and then the non-collocated observation is input into the right boundary to obtain the closed-loop system. The well-posedness of closed-loop system is proved by using the Riesz basis method. By using the Nyquist criterion, the admissible non-collocated feedback gain is concluded so that all eigenvalues of the closed-loop system are in the left-half complex plane, and the exponential stability of the closed-loop system is proved. The effectiveness of the proposed feedback control law is verified by numerical simulation.