ON CONES AND STABILITY

Lyapunov, while studying the asymptotic stability of solutions of diff erential systems, proved a theorem which yields a necessary and suffic ient condition for stability of a matrix. Lyapunov's theorem was a bre akthrough in the research of stability. Among others, it links cones a nd stability in Various directions. In this survey we review some of t he links between convexity and matrix stability, mainly such links tha t are derived from Lyapunov's theorem. The article does not cover the wide variety of all such links, but rather gives some of the flavor of this rich theory. (C) 1998 Elsevier Science Inc. All rights reserved.