# LMIs in Control/Matrix and LMI Properties and Tools/Young’s Relation (Completion of the Squares)

This method is used to solve quadratic equations that can't be factorized.

**Matrix inequality**Edit

Consider and , where >0, The matrix inequality given by

which is named Young’s relation or Young’s inequality.

**Derivation**Edit

Young’s relation can be derived from a completion of the squares as follows.

which is named Young’s relation.

**Reformulation of Young’s Relation**Edit

Consider and , where >0, The matrix inequality given by

is a reformulation of Young’s relation.

## External LinksEdit

A list of references documenting and validating the LMI.

- 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 List of LMIs by Ryan Caverly and James Forbes. (2.4.1 page 23)