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 ComplementsEdit

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 LemmaEdit

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 LinksEdit

A list of references documenting and validating the LMI.


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