Abstract
If a closed subset K is not a viability domain, the question arises as to whether there are closed viability subsets of K viable under F and even, whether there exists a largest closed subset of K viable under F. The answer is positive for Marchaud maps, and we call viability kernel of a closed subset K the largest closed subset viable under F contained in K. Actually, we shall prove in the first section that it is equal to the set of initial states of K from which there exists at least one solution viable in K.
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Aubin, JP. (2009). Viability Kernels and Exit Tubes. In: Viability Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4910-4_6
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DOI: https://doi.org/10.1007/978-0-8176-4910-4_6
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