LMIs in Control/Matrix and LMI Properties and Tools/Finsler's Lemma

LMIs in Control/Matrix and LMI Properties and Tools/Finsler's Lemma


This method It states equivalent ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. It is equivalent to other lemmas used in optimization and control theory, such as Yakubovich's S-lemma, Finsler's lemma and it is wedely used in Linear Matrix Inequalities


TheoremEdit

Consider  and  . There exists   such that

 

if and only if there exists   such that

 

 

Alternative Forms of Finsler's LemmaEdit

Consider  and  . If there exists   such that

 


holds for all    satisfying  , then there exists   such that

 

Modified Finsler's LemmaEdit

Consider  and  , where   is less that on equal to  , and  . There exists   such that

 

there exists   such that

 

ConclusionEdit

In summary, a number of identical methods have been stated above to determine the positive definiteness of LMIs.


External LinksEdit

A list of references documenting and validating the LMI.


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