Stabilization of unbounded bilinear control systems in Hilbert space |
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Authors: | Larbi Berrahmoune |
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Affiliation: | Département de Mathématiques, Ecole Normale Supérieure de Rabat, BP 5118, Rabat, Morocco |
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Abstract: | We consider bilinear control systems of the form y′(t)=Ay(t)+u(t)By(t) where A generates a strongly continuous semigroup of contraction (etA)t?0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. We suppose that this system is unbounded in the sense that the linear operator B is unbounded from the state Y into itself. Tacking into account eventual control saturation, we study the problem of stabilization by (possibly nonquadratic) feedback of the form u(t)=−f(〈By(t),y(t)〉). Applications to the heat equation is considered. |
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Keywords: | Unbounded bilinear system Stabilization Saturation |
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