Output-Feedback Stabilization of an Anti-stable Schrödinger Equation by Boundary Feedback with Only Displacement Observation

Authors:
Jun-Jun Liu;Jun-Min Wang
Affiliations:
School of Mathematics, Beijing Institute of Technology, Beijing, People's Republic of China 100081;School of Mathematics, Beijing Institute of Technology, Beijing, People's Republic of China 100081
Venue:
Journal of Dynamical and Control Systems
Year:
2013

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Abstract

We consider a problem of stabilization of a one-dimensional anti-stable linearized Schrödinger equation subject to boundary control. The controller is designed through the estimated state and is designed in the case that only displacement is available. The method of "backstepping" is adopted in the investigation. We then combine the control and observer designs into an output-feedback compensator and prove exponential stability of the closed-loop system.