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 Consider and . There exists such that if and only if there exists such that Alternative Forms of Finsler's Lemma Consider and . If there exists such that holds for all ≠ satisfying , then there exists such that Modified Finsler's Lemma Consider and , where is less that on equal to , and . There exists such that there exists such that Conclusion In summary, a number of identical methods have been stated above to determine the positive definiteness of LMIs. External Links 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. Return to Main Page: