The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control

The stabilization of a one-dimensional wave equation with non-collocated observation at its unstable free end and control at another end is considered. The controller comprises a state estimator which is designed in the case where the velocity is not available. The method of “backstepping” is adopted in our design of the feedback law. We use the theory of C 0 -semigroups and Lyapunov functionals to prove the strong stability of the resulting closed-loop system.