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Nonlinear feedback stabilization of a rotating body-beam without damping

Boumediène CHENTOUF, Jean-François COUCHOURON (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Nonlinear Maps between Besov and Sobolev spaces

Philip Brenner, Peter Kumlin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an exceptional low dimensional phenomenon. This extends previous results by Kumlin [13] from the case of analytic mappings to Lipschitz and Hölder continuous maps (Corollaries 1 and 2), and which go back to ideas of the late B.E.J. Dahlberg [8].

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