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
N1 - Funding Information:
The authors are grateful to the referees for their useful remarks and helpful suggestions. The first author also acknowledges the support of Sultan Qaboos University.
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
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U2 - 10.1016/j.jmaa.2005.06.003
DO - 10.1016/j.jmaa.2005.06.003
M3 - Article
AN - SCOPUS:33645066907
SN - 0022-247X
VL - 318
SP - 667
EP - 691
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -