Regional stabilization of linear delayed Schrödinger equation by constrained boundary control

This paper deals with the design of constrained control to stabilize the delayed Schrödinger equation with bounded internal disturbance. The state feedback control law is designed by using the backstepping method. Input-to-state stability (ISS) of the perturbed system with time-delay is established by a generalized Halanay inequality. We find an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to a bounded set. A numerical example illustrates the efficiency of the method.