Abstract
The present paper shows that the closure of the bounded control set of a linear control system contains all the bounded orbits of the system. As a consequence, we prove that the closure of this control set is the continuous image of the cartesian product of the set of control functions by the central subgroup associated with the drift of the system.
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Acknowledgements
The first author was supported by Proyecto Fondecyt n\(^{o}\) 1190142, Conicyt, Chile and the second author was supported by Fapesp Grants n\(^{o}\) 2020/12971-4 and partially by CAPES Grant No. 309820/2019-7.
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Víctor Ayala- Supported by Proyecto Fondecyt \(n^{o}\) 1190142, Conicyt, Chile. Adriano Da Silva- Supported by Fapesp Grant \(n^{o}\) 2020/12971-4, and partially by CNPq Grant No. 309820/2019-7.
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Ayala, V., Da Silva, A. On the structural properties of the bounded control set of a linear control system. Nonlinear Differ. Equ. Appl. 29, 53 (2022). https://doi.org/10.1007/s00030-022-00784-1
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DOI: https://doi.org/10.1007/s00030-022-00784-1