LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Young’s Relation (Completion of the Squares)
This method is used to solve quadratic equations that can't be factorized.
Matrix inequality
editConsider and , where >0, The matrix inequality given by
which is named Young’s relation or Young’s inequality.
Derivation
editYoung’s relation can be derived from a completion of the squares as follows.
which is named Young’s relation.
Reformulation of Young’s Relation
editConsider and , where >0, The matrix inequality given by
is a reformulation of Young’s relation.
External Links
editA 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)