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
[edit | edit source]Consider the matricies , , be symmetric. Then, there exists a symmetric matrix such that
if and only if
.
Lemma 2
[edit | edit source]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
External Links
[edit | edit source]A list of references documenting and validating the LMI.
- [1] - LMI in Control Systems Analysis, Design and Applications