An abstract setting for the Fredholm backstepping transformation: self-adjoint case
Résumé
In this paper we address the existence of a Fredholm backstepping transformation for self-adjoint operators A. We prove, under assumptions on the control operator B and A, that there exists a Fredholm backstepping transformation for operators A of order strictly greater than 1. One of the main contribution of the paper is to exhibit the underlying isomorphism used to construct T . This isomorphism allows to deduce sharp estimates on ∥T ∥ L(H;H) and ∥T -1 ∥ L(H;H) with respect to the damping parameter λ > 0. This allow us to prove the finite-time stabilization for a large class of self-adjoint operators.
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