Rapid stabilization of general linear systems with $F$-equivalence
Résumé
We study the rapid stabilization of general linear systems, when the differential operator $\mathcal{A}$ has a Riesz basis of eigenvectors. We find simple sufficient conditions for the rapid stabilization and the construction of a relatively explicit feedback operator. We use an $F$-equivalence approach relying on Fredholm transformation to show a stronger result: under these sufficient conditions %simple sufficient conditions so that there exists a constructive feedback operator that the system is equivalent to a simple exponentially stable system, with arbitrarily large decay rate. In particular, our conditions improve the existing conditions of rapid stabilization for non-parabolic operators such as skew-adjoint systems.
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