The minimal dimension of stable faces required to guaranteestability of a matrix polytope |
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Authors: | Cobb J.D. Demarco C.L. |
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Affiliation: | Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI; |
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Abstract: | Considers the problem of determining whether each point in a polytope n×n matrices is stable. The approach is to check stability of certain faces of the polytope. For n⩾3, the authors show that stability of each point in every (2n-4)-dimensional face guarantees stability of the entire polytope. Furthermore, they prove that, for any k⩽n2, there exists a k-dimensional polytope containing a strictly unstable point and such that all its subpolytopes of dimension min {k-1,2n-5} are stable |
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