Journal of Applied Mathematics
Volume 2004 (2004), Issue 2, Pages 107-126

Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity

Boumediène Chentouf

Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Oman

Received 7 December 2003; Revised 24 February 2004

Copyright © 2004 Boumediène Chentouf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with feedback stabilization of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the rigid body rotates with a nonconstant angular velocity. To stabilize this system, we propose a feedback law which consists of a control torque applied on the rigid body 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. Then it is shown that the closed loop system is well posed and exponentially stable provided that the actuators, which generate the boundary controls, satisfy some classical assumptions and the angular velocity is smaller than a critical one.