### Abstract

This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear case studied by Laousy et al. to a more general class of controls.

Original language | English |
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Pages (from-to) | 515-535 |

Number of pages | 21 |

Journal | ESAIM - Control, Optimisation and Calculus of Variations |

Issue number | 4 |

Publication status | Published - 1999 |

### Fingerprint

### Keywords

- Exponential stability
- Nonlinear control
- Rotating body-beam

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*ESAIM - Control, Optimisation and Calculus of Variations*, (4), 515-535.

**Nonlinear feedback stabilization of a rotating body-beam without damping.** / Chentouf, B.; Couchouron, J. F.

Research output: Contribution to journal › Article

*ESAIM - Control, Optimisation and Calculus of Variations*, no. 4, pp. 515-535.

}

TY - JOUR

T1 - Nonlinear feedback stabilization of a rotating body-beam without damping

AU - Chentouf, B.

AU - Couchouron, J. F.

PY - 1999

Y1 - 1999

N2 - This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear case studied by Laousy et al. to a more general class of controls.

AB - This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear case studied by Laousy et al. to a more general class of controls.

KW - Exponential stability

KW - Nonlinear control

KW - Rotating body-beam

UR - http://www.scopus.com/inward/record.url?scp=0033276587&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033276587&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033276587

SP - 515

EP - 535

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

IS - 4

ER -