LMIs in Control/pages/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 $\mathrm{\Phi }\in {𝕊}^n$, there exists a matrix $S\in {ℝ}^{n\times n}$ satisfying

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

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

$\left[\begin{array}{cc}\mathrm{\Phi }+P-(W^T+W)& S^T+W^T\\ S+W& -P\end{array}\right]<0$.

WIP, additional references to be added

External Links

A list of references documenting and validating the LMI.