LMIs in Control/Matrix and LMI Properties and Tools/Young’s Relation (Completion of the Squares)
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This method is used to solve quadratic equations that can't be factorized.
Matrix inequality[edit | edit source]
Consider and , where >0, The matrix inequality given by
which is named Young’s relation or Young’s inequality.
Derivation[edit | edit source]
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 | edit source]
Consider and , where >0, The matrix inequality given by
is a reformulation of Young’s relation.
External Links[edit | edit source]
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)