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Strong stabilization of controlled vibrating systems
Published online by Cambridge University Press: 08 November 2010
Abstract
This paper deals with feedback stabilization of second order equations ofthe form
ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[,
where A0 is a densely defined positive selfadjoint linear operator on areal Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It isproved here that the classical sufficient ad-condition of Jurdjevic-Quinn andBall-Slemrod with the feedback control u = ⟨yt, B0y⟩Himplies thestrong stabilization. This result is derived from a general compactnesstheorem for semigroup with compact resolvent and solves several open problems.
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- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 1144 - 1157
- Copyright
- © EDP Sciences, SMAI, 2010
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