en
2019-04-01
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.
https://link.springer.com/10.1007%2Fs10883-018-9414-y
2019-04
research_article
275-288
2019-04-11T13:20
Stabilization of One-Dimensional Schrödinger Equation Under Joint Feedback Control with Delayed Observation
false
https://scigraph.springernature.com/explorer/license/
articles
a81414895653c717873503819d384d634276213fcdb157599b1ed0308e4cdaf5
readcube_id
K. Y.
Yang
College of Science, North China University of Technology, Beijing, China
North China University of Technology
doi
10.1007/s10883-018-9414-y
1079-2724
1573-8698
Journal of Dynamical and Control Systems
Applied Mathematics
dimensions_id
pub.1105708945
Mathematical Sciences
25
2
Springer Nature - SN SciGraph project