# LMIs in Control/pages/Schur Complement

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An important tool for proving many LMI theorems is the Schur Compliment. It is frequently used as a method of LMI linearization.

**The Schur Compliment**[edit]

Consider the matricies , , and where and are self-adjoint. Then the following statements are equivalent:

- and both hold.
- and both hold.
- is satisfied.

More concisely:

## External Links[edit]

- 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.