Boundary Feedback Stabilization of a Variant of the SCOLE Model

Authors:
Boumediène Chentouf
Affiliations:
Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Sultanate of Oman. E-mail: chentouf@squ.edu.om
Venue:
Journal of Dynamical and Control Systems
Year:
2003

Citing 2
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Abstract

This paper deals with the boundary feedback stabilization of a variant of the SCOLE model, namely, a flexible beam clamped at one end, and free at the other end where a rigid body is attached. Using the frequency domain method, we first prove that the considered system is uniformly stabilizable if the control force and control moment are simultaneously applied at the free end of the beam. Secondly, if only a control force is applied, we give a sufficient condition on the physical parameters of the system to guarantee the uniform stabilization. Finally, it is shown that the presence of boundary control force is necessary to achieve the uniform stabilization. To verify these theoretical developments, an asymptotic analysis and numerical study of the spectrum are performed.