Stabilisation of nonlinear ODE and wave PDE cascaded systems with damping terms

Abstract

We investigate asymptotically stabilisation for the cascaded system of a nonlinear ODE and a wave PDE with damping terms by a predictor control. Based on the backstepping transformations, the cascaded system is transferred to a target system. Further, a predictor control is designed. It is proved that the target system is asymptotically stable by using a Lyapunov functional. Further the stability of the original system under the proposed control law is equivalent to that of the target system. An example is given to illustrate the validity of the proposed method.