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LMIs in Control/Tools/Elimination of Variables/Variable Elimination in a Partition Matrix

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WIP, Description in progress

Two basic lemmas treat the elimination of variables in a partitioned matrix.

Lemma 1

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Consider the matricies , , be symmetric. Then, there exists a symmetric matrix such that

if and only if

.

Lemma 2

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Let , , be given matrices of appropriate dimensions. Then there exists a matrix such that

if and only if

,

In this case, is given by

.

WIP, additional references to be added

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A list of references documenting and validating the LMI.

  • [1] - LMI in Control Systems Analysis, Design and Applications

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