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Stabilizability of infinite-dimensional systems by finite-dimensional controls. (English) Zbl 1432.93263
Comput. Methods Appl. Math. 19, No. 4, 797-811 (2019); retraction ibid. 20, No. 2, 395 (2020).
Summary: In this paper, we consider control systems for which the underlying semigroup is analytic, and the resolvent of its generator is compact. In that case we give a characterization of the stabilizability of such control systems. When the stabilizability condition is satisfied the system is also stabilizable by finite-dimensional controls. We end the paper by giving an application of this result to the stabilizability of the Oseen equations with mixed boundary conditions.
Editorial remark: From the text of the retraction notice: “The Editors and the Publisher of Computational Methods in Applied Mathematics retract from publication this article. Due to technical reasons and the erroneous assignment of different DOI numbersan identical version of this paper was published in an earlier issue of the journal [J.-P. Raymond, Comput. Methods Appl. Math. 19, No. 2, 267–282 (2019; Zbl 1422.93158)]. Hence the version of thearticle that was published later is herewith retracted.”

##### MSC:
 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C25 Control/observation systems in abstract spaces 93B52 Feedback control 93C20 Control/observation systems governed by partial differential equations 76D55 Flow control and optimization for incompressible viscous fluids
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