% The dual of a subset of an inner-product space; always a closed
% convex cone.
-\newcommand*{\dual}[1]{ {#1}^{*} }
+\newcommand*{\dual}[1]{ #1^{*} }
%
% Common cones.
% The space of Lyapunov-like operators on its argument.
\newcommand*{\LL}[1]{ \mathbf{LL}\of{ {#1} } }
+% The Lyapunov rank of the given cone.
+\newcommand*{\lyapunovrank}[1]{ \beta\of{ {#1} } }
%
% Cone inequality operators.