LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Reciprocal Projection Lemma

WIP, Description in progress

Another condition for eliminating a variable in an LMI called reciprocal projection lemma is introduced.

Reciprocal Projection Lemma

For a given symmetric matricx $\Phi \in \mathbb {S} ^{n}$, there exists a matrix $S\in \mathbb {R} ^{n\times n}$ satisfying

$\Phi +S^{T}+S<0$

if and only if, for an arbitrarily fixed symmetric matrix $P\in \mathbb {S} ^{n}$, there exist a matrix $W\in \mathbb {R} ^{n\times n}$ satisfying

${\begin{bmatrix}\Phi +P-(W^{T}+W)&S^{T}+W^{T}\\S+W&-P\end{bmatrix}}<0$.

WIP, additional references to be added

External Links

A list of references documenting and validating the LMI.