Necessary and sufficient conditions are given for robust stability of a family of polynomials. Each polynomial is obtained by a multilinearity perturbation structure. Restrictions on the multilinearity are involved, but, in contrast to existing literature, these restrictions are derived from physical considerations stemming from analysis of a closed-loop interval feedback system. The main result indicates that all polynomials in the family of polynomials have their zeros in the strict left half-plane if and only if two requirements are satisfied at each frequency. The first requirement is the zero exclusion condition involving four Kharitonov rectangles. The second requirement is that a specially constructed theta 0-parameterized set of 16 intervals must cover the positive reals for each theta epsilon (0,2 pi ).
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