LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Submatrix Determinants and Imaginary and Real Parts
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Submatrix Determinants
[edit | edit source]Required data
[edit | edit source]Consider , Let be a submatrix of A consisting of its first rows and columns, where .
Matrix inequality
[edit | edit source]The matrix inequality is satisfied if and only if
.
Imaginary and Real Parts
[edit | edit source]Required data
[edit | edit source]Consider , , ,
Matrix inequality
[edit | edit source]The matrix inequality, is equivalent to the matrix inequality given by
.
External Links
[edit | edit source]- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.