A critical-point criterion for D-stability in every dimension
A real square matrix A is D-stable if DA is Hurwitz for every positive diagonal matrix D. Applying the critical-point method to Johnson’s contact variety establishes that, in every dimension and for every positive choice of barrier weights, D-stability is equivalent to Hurwitz stability and absence of positive solutions of an explicit principal-minor Fritz–John system. In dimension five the system separates into Lagrange and tangency branches; both equivalences are registered in Lean. Further results treat regular-contact persistence, the boundary of the D-stable set, stability under bounded…
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