mjo-cone.tex

   1 %
   2 % Cone stuff.
   3 %
   4 % The operator families Z(K), LL(K), etc. can technically be defined on
   5 % sets other than cones, but nobody cares.
   6 %
   7
   8 \usepackage{amssymb} % \succcurlyeq and friends
   9
  10 \input{mjo-common}
  11
  12 % The set of all S-operators on its argument.
  13 \newcommand*{\Sof}[1]{ \mathbf{S} \of{ {#1} } }
  14
  15 % The cone of all Z-operators on its argument.
  16 \newcommand*{\Zof}[1]{ \mathbf{Z} \of{ {#1} } }
  17
  18 % The space of Lyapunov-like operators on its argument.
  19 \newcommand*{\LL}[1]{ \mathbf{LL}\of{ {#1} } }
  20
  21 % Cone inequality operators.
  22 \newcommand*{\gek}{ \succcurlyeq }
  23 \newcommand*{\gtk}{ \succ }
  24 \newcommand*{\lek}{ \preccurlyeq }
  25 \newcommand*{\ltk}{ \prec }
  26
  27 % Starred versions of the cone inequality operators.
  28 \newcommand*{\ineqkstar}[1]{ \mathrel{ \overset{ _{\ast} }{ #1 } } }
  29 \newcommand*{\gekstar}{ \ineqkstar{\gek} }
  30 \newcommand*{\gtkstar}{ \ineqkstar{\gtk} }
  31 \newcommand*{\lekstar}{ \ineqkstar{\lek} }
  32 \newcommand*{\ltkstar}{ \ineqkstar{\ltk} }
  33
  34 % And negated versions of some of those...
  35 \newcommand*{\ngeqkstar}{ \ineqkstar{\nsucceq} }
  36 \newcommand*{\ngtrkstar}{ \ineqkstar{\nsucc} }