LMIs in Control/Matrix and LMI Properties and Tools/Dualization Lemma

Dualization LemmaEdit

Consider   and the subspaces  , where   is invertible and  . The following are equivalent.

  for all  \  and   for all  .

  for all  \  and   for all  .

ExampleEdit

Consider the matrices   where   which define the quadratic matrix inequality

 

Define   where  . Notice that   is equivalent to   for all  \ .Additionally,   for all   is euaivalent to

 

which is satisfied based on the definition of   . By the dualization lemma,   is satisfied with   if and only if

 

where   , and  .

External LinksEdit