Geodesic
Stabilization of Euler-Bernoulli beam equations with variable coefficients under delayed boundary output feedback
Electronic journal of differential equations, Tome 2015 (2015)
In this article, we study the stabilization of an Euler-Bernoulli beam equation with variable coefficients where boundary observation is subject to a time delay. To resolve the mathematical complexity of variable coefficients, we design an observer-predictor based on the well-posed open-loop system: the state of system is estimated with available observation and then predicted without observation. We show that the closed-loop system is stable exponentially under estimated state feedback by a numerical simulation illustrating our results.
Classification : 35J10, 93C20, 93C25
Keywords: Euler-Bernoulli beam equation, variable coefficients, time delay, observer, feedback control, exponential stability 
@article{EJDE_2015__2015__a77,
     author = {Yang,  Kun-Yi and Li,  Jing-Jing and Zhang,  Jie},
     title = {Stabilization of {Euler-Bernoulli} beam equations with variable coefficients under delayed boundary output feedback},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1315.35066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a77/}
}
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%A Zhang,  Jie
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%J Electronic journal of differential equations
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%F EJDE_2015__2015__a77
Yang,  Kun-Yi; Li,  Jing-Jing; Zhang,  Jie. Stabilization of Euler-Bernoulli beam equations with variable coefficients under delayed boundary output feedback. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a77/