Stabilization of Distributed Parameter Systems With Delays in the Boundary Based on Predictors

This article is concerned with the controller design for distributed parameter systems with time delays in the boundary. An implementable control law is presented in light of a state predictor, and a feasible calculation scheme of this control law is provided based on the adjoint theory. The resulting closed-loop system is proved to be exponentially stable. As an application, a one-dimensional Schrödinger equation with a delay input is introduced and the numerical simulation verifies the feasibility of the suggested control law.