Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control

Abstract

In this paper, the uniform stabilization of a multi-dimensional Schrödinger equation with partial Dirichlet delayed control is concerned. The control input is suffered from time delay. Herein a new feedback controller is adopted in the investigation. Firstly, we rewrite the delayed system under consideration into a cascaded system of a transport equation and a Schrödinger equation, and construct an exponentially stable target system. Then by defining a bounded invertible linear transformation and choosing some appropriate kernel functions, we establish the equivalence between the closed-loop system and the target system. Finally, the exponential stability of the closed-loop system is obtained.