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LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Projection Lemma (Matrix Elimination Lemma)
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WIP, Description in progress
A condition for eliminating a variable in an LMI using orthogonal complements is presented.
Definition 1: Orthogonal Complements
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
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
A list of references documenting and validating the LMI.
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