Disturbance Rejection in Boundary Control Systems

An elastic string subjected to external disturbance and stabilized by the boundary control is considered. The problem of optimal disturbance rejection by the boundary control is formulated. Furthermore, it is shown that, any strictly positive real compensator in the boundary control stabilizes the string. This fact results in the formulation of optimal disturbance rejection for an elastic string, when strictly positive real compensators are used in the boundary control.