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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.

Keyword : Backstepping transformation, boundary control, nonlocal term, output feedback, Schrödinger equation.

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