A critical-point criterion for D-stability in every dimension
Year: 2026
Type: preprint
Abstract: 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, we prove, for every dimension and every positive choice of barrier weights, that 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 time-scale ratios and the minimal destabilizing ratio. The finite decision procedure also uses conventional finiteness and termination arguments and was executed exactly only in dimension three. For the five-dimensional Lagrange system the multihomogeneous Bézout number is 1200; 980 generic complex solutions were observed numerically. Worked examples include a Lotka–Volterra community, a published refinery-column gain matrix and an exactly recovered benchmark window. Formal statements, conventional arguments, exact certificates and numerical illustrations are distinguished throughout.
Author: Mislan, Michael
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222866100
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