|Boundary Output Feedback Stabilization of the Linearized Schrödinger Equation with Nonlocal Term
Liping Wang and Feng-Fei Jin*
International Journal of Control, Automation, and Systems, vol. 19, no. 4, pp.1528-1538, 2021
Abstract : In this paper, we are concerned with the boundary output feedback stabilization problem of a Schrödinger equation with a nonlocal term. Firstly, we design an explicit boundary state feedback controller by backstepping approach. Under this controller, the closed-loop system is proved to be exponentially stable from the equivalence between the original system and the target system. Then, we propose an observer-based output feedback controller by replacing the state in state feedback controller with its estimation. The resulting closed-loop system admits a unique solution which is exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.
Backstepping transformation, boundary control, nonlocal term, output feedback, Schrödinger equation.
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