Boundary Constrained Control of Delayed Nonlinear Schrödinger Equation

This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-to-state stability of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay's inequality. Estimates on the set of initial conditions are found starting from which the solutions are exponentially attracted to a bounded set. A numerical example demonstrates the efficiency of the results.