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2005 Boundary stabilization of a flexible manipulator with rotational inertia
Bao-Zhu Guo, Jun-Min Wang, Siu-Pang Yung
Differential Integral Equations 18(9): 1013-1038 (2005).

Abstract

We design a stabilizing linear boundary feedback control for a one-link flexible manipulator with rotational inertia. The system is modelled as a Rayleigh beam rotating around one endpoint, with the torque at this endpoint as the control input. The closed-loop system is nondissipative, so that its well posedness is not easy to establish. We study the asymptotic properties of the eigenvalues and eigenvectors of the corresponding operator $\mathcal A$ and establish that the generalized eigenvectors form a Riesz basis for the energy state space. It follows that $\mathcal A$ generates a $C_0$-semigroup that satisfies the spectrum-determined growth assumption. This semigroup is exponentially stable under certain conditions on the feedback gains. If the higher-order feedback gain is set to zero, then we obtain a polynomial decay rate for the semigroup.

Citation

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Bao-Zhu Guo. Jun-Min Wang. Siu-Pang Yung. "Boundary stabilization of a flexible manipulator with rotational inertia." Differential Integral Equations 18 (9) 1013 - 1038, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.93254
MathSciNet: MR2162985

Subjects:
Primary: 93D15
Secondary: 35P10, 35Q72, 47D06, 70E60, 74M05, 93C85

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 9 • 2005
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