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Compact perturbations of controlled systems

Abstract : 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.
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Submitted on : Thursday, July 27, 2017 - 10:24:22 PM
Last modification on : Thursday, January 23, 2020 - 6:22:13 PM

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  • HAL Id : hal-01406540, version 2

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Michel Duprez, Guillaume Olive. Compact perturbations of controlled systems. Mathematical Control and Related Fields, AIMS, 2018, 8 (2), pp.397-410. ⟨hal-01406540v2⟩

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