On cones and stability Original Research Article

Lyapunov, while studying the asymptotic stability of solutions of differential systems, proved a theorem which yields a necessary and sufficient condition for stability of a matrix. Lyapunovʹs theorem was a breakthrough in the research of stability. Among others, it links cones and stability in various directions. In this survey we review some of the links between convexity and matrix stability, mainly such links that are derived from Lyapunovʹs theorem. The article does not cover the wide variety of all such links, but rather gives some of the flavor of this rich theory.