Sliding Mode Control to Wave Equation with Velocity Recirculation and Matched Disturbance

In this paper, the stabilization problem of one-dimensional wave equation with velocity recirculation and matched disturbance is studied. The sliding model control (SMC) and backstepping method are applied to handle the disturbance. Firstly, we propose a variable structure control law. Under the designed control law, the resulting closed-loop has a unique solution and the solution decays exponentially. At last, we validate the effectiveness of designed method by giving the numerical experiments.