LMIs in Control/pages/Projection Lemma

WIP, Description in progress

A condition for eliminating a variable in an LMI using orthogonal complements is presented.

Definition 1: Orthogonal Complements edit

Let  , Then,   is called a left orthogonal complement of   if it satisfies

 ;

and   is called a right orthogonal complement of   if it satisfies

 .

Using the definition of orthogonal complements, we have the following projection lemma:

Projection Lemma edit

Let  ,   and   be given matrices of appropriate dimensions,   and   be the right orthogonal complement of   and  , respectively. Then, there exists   such that

 

if and only if

 .

WIP, additional references to be added

External Links edit

A list of references documenting and validating the LMI.


Return to Main Page: edit