Controller Design and Stability Analysis for Schrödinger Equation Subject to a Restricted Boundary Feedback

Design of controller subject to a constraint for a Schrödinger equation is considered. The controller is deduced based on the energy functional of the system. As the resulting system is nonlinear, the monotone operator theory and a complex form of the nonlinear Lax-Milgram theorem are adopted to prove the well-posedness. With the LaSalle invariance principle, the asymptotic stability of the system is obtained.