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Compact perturbations of controlled systems

  • * Corresponding author: Guillaume Olive

    * Corresponding author: Guillaume Olive
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  • In this article we study the controllability properties of general compactly perturbed exactly controlled linear systems with admissible control operators. Firstly, we show that approximate and exact controllability are equivalent properties for such systems. Then, and more importantly, we provide for the perturbed system a complete characterization of the set of reachable states in terms of the Fattorini-Hautus test. The results rely on the Peetre lemma.

    Mathematics Subject Classification: Primary: 93B05, 93C73; Secondary: 93C73.


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