Abstract
In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 667-691 |
| Number of pages | 25 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 318 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 15 2006 |
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Keywords
- Dynamic boundary control
- Exponential stability
- Frequency multiplier method
- Non-homogeneous coefficients
- Riesz basis
- Rotating body-beam
- Spectral analysis
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls. / Chentouf, Boumediène; Wang, Jun Min.
In: Journal of Mathematical Analysis and Applications, Vol. 318, No. 2, 15.06.2006, p. 667-691.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls
AU - Chentouf, Boumediène
AU - Wang, Jun Min
PY - 2006/6/15
Y1 - 2006/6/15
N2 - In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.
AB - In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.
KW - Dynamic boundary control
KW - Exponential stability
KW - Frequency multiplier method
KW - Non-homogeneous coefficients
KW - Riesz basis
KW - Rotating body-beam
KW - Spectral analysis
UR - http://www.scopus.com/inward/record.url?scp=33645066907&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33645066907&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2005.06.003
DO - 10.1016/j.jmaa.2005.06.003
M3 - Article
VL - 318
SP - 667
EP - 691
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -