LMIs in Control/Matrix and LMI Properties and Tools/Continuous Time/Schur Complement/Strict Schur Complement

Strict Schur Complement

Consider $A\in \mathbb {S} ^{n},B\in \mathbb {R} ^{n\times m},$ and $C\in \mathbb {S} ^{m}.$ The following statements are equivalent.

a) ${\begin{bmatrix}A&B\\B^{T}&C\end{bmatrix}}<0$

b) $A-BC^{-1}B^{T}<0,C<0$

c) $C-B^{T}A^{-1}B<0,A<0$

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.