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Stabilization of One‐Dimensional Schrödinger Equation with Variable Coefficient under Delayed Boundary Output Feedback
Author(s) -
Yang KunYi,
Yao CuiZhen
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.667
Subject(s) - variable coefficient , control theory (sociology) , observer (physics) , variable (mathematics) , mathematics , boundary (topology) , boundary value problem , state variable , controller (irrigation) , interval (graph theory) , state observer , mathematical analysis , physics , control (management) , computer science , nonlinear system , quantum mechanics , combinatorics , artificial intelligence , biology , agronomy , thermodynamics
This article considers stabilization of a one‐dimensional Schrödinger equation with variable coefficient and boundary observation which suffers from an arbitrary given time delay. We design an observer and predictor to stabilize the system. The state is estimated in the time span where the observation is available, and also predicted in the time interval where the observation is not available. It is shown that the estimated state feedback stabilizes the system exponentially. A numerical simulation is presented to illustrate the effect of the stabilizing controller.