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LMIs in Control/Tools/Notion of Matrix Positivity
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Notation of Positivity
A symmetric matrix is defined to be:
positive semidefinite, , if for all .
positive definite, , if for all .
negative semidefinite, .
negative definite, .
indefinite if is neither positive semidefinite nor negative semidefinite.
Properties of Positive Matricies
For any matrix , .
Positive definite matricies are invertible and the inverse is also positive definite.
A positive definite matrix has a square root, , such that .
For a positive definite matrix and invertible , .
If and , then .
If then for any scalar .
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External Links
LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.