TY - JOUR
T1 - Optimal energy decay for a nonhomogeneous flexible beam with a tip mass
AU - Chentouf, Boumediène
AU - Wang, Jun Min
N1 - Funding Information:
2000 Mathematics Subject Classification. 35B35, 35P20, 47D03, 93C20, 93D15. Key words and phrases. Nonhomogeneous beam, boundary control, Riesz basis, uniform stability, spectrum-determined growth condition, optimal energy decay. The first author acknowledges the support of Sultan Qaboos University. The second author is supported by the National Natural Science Foundation of China.
PY - 2007/1
Y1 - 2007/1
N2 - In this paper, a simple boundary feedback control moment is proposed to stabilize a nonhomogeneous flexible beam with a tip mass. By adopting the Riesz basis approach, it is shown that the close-loop system is a Riesz spectral system. Consequently, the exponential stability, spectrum-determined growth condition, and optimal decay rate are obtained.
AB - In this paper, a simple boundary feedback control moment is proposed to stabilize a nonhomogeneous flexible beam with a tip mass. By adopting the Riesz basis approach, it is shown that the close-loop system is a Riesz spectral system. Consequently, the exponential stability, spectrum-determined growth condition, and optimal decay rate are obtained.
KW - Boundary control
KW - Nonhomogeneous beam
KW - Optimal energy decay
KW - Riesz basis
KW - Spectrum-determined growth condition
KW - Uniform stability
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U2 - 10.1007/s10883-006-9002-4
DO - 10.1007/s10883-006-9002-4
M3 - Article
AN - SCOPUS:33847636087
SN - 1079-2724
VL - 13
SP - 37
EP - 53
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
IS - 1
ER -