A General Non-Strict Finsler's Lemma

In this paper, we present a general non-strict Finsler's lemma. This result is general in the sense that it does not impose any restrictions on the involved matrices and, thereby, is more broadly applicable than existing non-strict versions of Finsler's lemma that do impose such restrictions. In fact, we show that this new non-strict formulation generalizes both the original strict Finsler's lemma as well as an existing non-strict version. To further illustrate its usefulness, we showcase applications of the non-strict Finsler's lemma in deriving a closed-form solution to the non-strict projection lemma, and a matrix Finsler's lemma, which is useful for data-driven control.