Finsler's lemma is a mathematical result named after Paul Finsler. It states equivalent ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. Since it is equivalent to another lemmas used in optimization and control theory, such as Yakubovich's S-lemma,[1] Finsler's lemma has been given many proofs and has been widely used, particularly in results related to robust optimization and linear matrix inequalities.