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 inequalityEdit

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

 

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

DerivationEdit

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

 

which is named Young’s relation.

Reformulation of Young’s RelationEdit

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.


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