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A critical-point criterion for D-stability in every dimension

Michael Mislan

Palomar Registrypalomar/PALOMAR-2026-09-30-000020Sep 30, 2026math.DSscore 0

Johnson's contact criterion for D-stability is expressed as an explicit principal-minor critical-point system. For every real square matrix and every choice of positive barrier weights, D-stability is equivalent to Hurwitz stability and the absence of positive solutions of the associated Fritz-John equations. The proof applies a proper exhaustion of the positive orthant to Johnson's contact variety, so that every nonempty contact set contains a critical point. In dimension five, the criterion is written explicitly as a Lagrange system and a tangency system, with coefficients given by…

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