## Differential and Integral Equations

### Boundary stabilization of a flexible manipulator with rotational inertia

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 18, Number 9 (2005), 1013-1038.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060120

Mathematical Reviews number (MathSciNet)
MR2162985

Zentralblatt MATH identifier
1212.93254

#### Citation

Guo, Bao-Zhu; Wang, Jun-Min; Yung, Siu-Pang. Boundary stabilization of a flexible manipulator with rotational inertia. Differential Integral Equations 18 (2005), no. 9, 1013--1038. https://projecteuclid.org/euclid.die/1356060120