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>or=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<or=n/sup 2/, 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.<<ETX>>
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