Geodesic
The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem
The electronic journal of linear algebra, Tome 12 (2004-2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, the structure of several convex cones that arise in the study of Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both linear and non-linear systems are considered, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, some technical results are presented on the structure of individual cones and it is shown how these insights can lead to new results on the problem of common Lyapunov function existence.
Classification : 37B25, 47L07, 39B42
Keywords: Lyapunov functions and stability, convex cones, matrix equations 
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     author = {Mason, Oliver and Shorten, Robert},
     title = {The geometry of convex cones associated with the {Lyapunov} inequality and the common {Lyapunov} function problem},
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Mason, Oliver; Shorten, Robert. The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem. The electronic journal of linear algebra, Tome 12 (2004-2005). http://geodesic.mathdoc.fr/item/ELA_2004-2005__12__a2/