Abstract
A solution to an open research problem related to testing root exclusion of a real n-dimensional polynomial ( n ⩾ 1) from a subspace of Ĉ n [defined as a Cartesian product ( n times) of ( C ∪ ∞) × ( C ∪ ∞)…] is given in this paper. The solution is presented in two theorems which have application to several research problems, related to robust relative multidimensional stability. Among them are the testing of robust relative stability of linear differential systems, the testing of robust relative stability of linear delay differential systems, and a complementary test for a robust stabilization algorithm. Several examples are presented to illustrate some of these applications.
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