# 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

**Theorem**Edit

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

**Conclusion**Edit

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.

- 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 downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.