Abstract
In this paper, we study relationships among structural properties of min-max functions and complexity on deciding the sizes of the eigenspaces of minmax functions. We show that strong connectivity implies inseparability; Olsder’s separated systems are separable. A relaxed condition under which inseparability remains equivalent to the balance condition is also presented. The decision problem of whether the size of the eigenspace of a min-max function is greater than one is then report to be NP-hard based on the connection between the separability of a min-max function and the size of the eigenspace of its skeleton.
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Zhao, Q., Zheng, DZ. Note on Structural Properties and Sizes of Eigenspaces of Min-max Functions. In: Benvenuti, L., De Santis, A., Farina, L. (eds) Positive Systems. Lecture Notes in Control and Information Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44928-7_52
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DOI: https://doi.org/10.1007/978-3-540-44928-7_52
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40342-5
Online ISBN: 978-3-540-44928-7
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