A generalization of strong Kharitonov theorems to polytopes of polynomials

The root clustering property of a certain class of polytopes of polynomials is examined. It is shown that the polytopes of polynomials have only zeros within the left sector if and only if a subset of their edge polynomials has only zeros within the left sector. Certain conditions are derived under which the root clustering property of the polytopes of polynomials can be inferred from a subset of their vertices.<
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