Stabilization of One-Dimensional Schrödinger Equation Under Joint Feedback Control with Delayed Observation View Full Text


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Article Info

DATE

2019-04

AUTHORS

K. Y. Yang

ABSTRACT

In this paper, we consider a one-dimensional Schrödinger equation under a joint linear feedback control at an arbitrary internal point ξ(0<ξ<1). It is shown that the pointwise control system is asymptotically stable if ξ is either an irrational number or a rational number satisfying ξ≠2l/(2m−1) for any positive integers l,m(1≤l≤m−1); further, the system is exponentially stable if ξ is a rational number satisfying ξ≠2l/(2m−1) for any positive integers l,m(1≤l≤m−1). Moreover, we consider the Schrödinger equation under a joint feedback control where the observation is suffered from a given time delay. A Luenberger observer is designed at the time interval when the observation signal is available, while a predictor is designed at the time interval when the observation signal is not available. A natural control law is constructed based on the estimated state. The closed-loop system is shown to be exponentially stable for the smooth initial value. Finally, numerical simulations demonstrate effectiveness of the dynamic output feedback controller. More... »

PAGES

275-288

References to SciGraph publications

  • 2002-07. Decay Rates for a Beam with Pointwise Force and Moment Feedback in MATHEMATICS OF CONTROL, SIGNALS, AND SYSTEMS
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    http://scigraph.springernature.com/pub.10.1007/s10883-018-9414-y

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    http://dx.doi.org/10.1007/s10883-018-9414-y

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