Refined Wirtinger-type integral inequality

Based on the extreme value conditions of a multiple variables function, a new class of Wirtinger-type double integral inequality is established in this paper. The proposed inequality generalizes and refines the classical Wirtinger-based integral inequality and has less conservatism in comparison with Jensen’s double integral inequality and other double integral inequalities in the literature. Thus, the stability criteria for delayed control systems derived by the proposed refined Wirtinger-type integral inequality are less conservative than existing results in the literature.