Controller design to stabilization of Schrödinger equation with boundary input disturbance

ABSTRACTIn this paper, the stabilization problem of one-dimensional Schrodinger equation with boundary disturbance is concerned. The variable structure control technique is adopted to design the nonlinear feedback controller. For the Schrodinger system, the observation blind point problem is discussed and the relationship between the initial data and observation blind point is given. According to a theorem which can be regarded as an extended version of the Lions–Lax–Milgram theorem, the existence and uniqueness of the solution for the system are proved. Finally, a sufficient condition for the asymptotic stability of the system is provided. As a remark, the asymptotic stability, which can be realized by the control, is also presented.