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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