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 |
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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 |
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